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Veerle Van Doorsselaere

Health Monitoring systemsStudies on phased array actuators for aircraft Structural

Academiejaar 2007-2008Faculteit IngenieurswetenschappenVoorzitter: prof. dr. ir. Joris DegrieckVakgroep Mechanische constructie en productie

Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniekMasterproef ingediend tot het behalen van de academische graad van

Begeleider: prof. Agostinho Rui Alves da Fonseca Promotoren: prof. dr. ir. Joris Degrieck, prof. Afzal Suleman

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Veerle Van Doorsselaere

Health Monitoring systemsStudies on phased array actuators for aircraft Structural

Academiejaar 2007-2008Faculteit IngenieurswetenschappenVoorzitter: prof. dr. ir. Joris DegrieckVakgroep Mechanische constructie en productie

Master in de ingenieurswetenschappen: werktuigkunde-elektrotechniekMasterproef ingediend tot het behalen van de academische graad van

Begeleider: prof. Agostinho Rui Alves da Fonseca Promotoren: prof. dr. ir. Joris Degrieck, prof. Afzal Suleman

Preface

Time is money. In the aircraft industry, more money is going around and so this sentence iseven more important. Nevertheless great attention need to be payed to safety. For this, a strictschedule of inspections is followed. Nowadays a lot of these inspections happen when the plane ison the ground. If these inspections could be done while the plane is in the air, companies wouldsafe a lot of money. Nowadays this is not yet possible but a lot of engineers are investigating thepossibilities. I am happy I was one of them.

This work is not only the result of my interest in the subject. A lot of people, each in their ownway, helped me to finish this work in a proper way. People who supported me during my studiesand who made me the way I am today.

At first, I would like to say thanks to my thesis promoters prof. Fonseca and prof. Suleman forthe time they spend to guide me through this work. They encouraged me in my work and forcedme to go behind my limits.

Also I would like to thank prof. Degrieck and prof. Vantorre from Belgium. When I thought myerasmus year was going to fail, they helped me and made my dream come true.

People that I can not thank enough are my parents. They gave my the chances to develop myselflike I wanted during all this years.

Furthermore I want to say thanks to some people with whom I had some interesting contactsduring the development of my thesis: Bruno Rocha and Joana Roque Capinha. Thanks a lot.

Veerle Van Doorsselaere, June 2008

De auteur geeft de toelating deze masterproef voor consultatie beschikbaar te stellen en

delen van de masterproef te kopieren voor persoonlijk gebruik. Elk ander gebruik valt onder

de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting

de bron uitdrukkelijk te vermelden bij het aanhalen van resultaten uit deze masterproef.

9 juni 2008, Veerle Van Doorsselaere

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Summary

Structural Health Monitoring (SHM) is a research field that has been growing in the last years.SHM leads to the development of integrated systems capable of continuously monitoring struc-tures. The ultimate goal of SHM in aerospace engineering is to guarantee the safety of aircraftswith minimal costs. To achieve that, it is tried to perform the necessary tests while the plane isin the air. The sensors used in this tests will be ideally embedded in the structure.

Structural flaws represent changes in effective thickness and local material properties. Lambwaves can be used to detect these changes. Therefore measurements of variations in Lamb wavepropagation can be employed to assess the integrity of the structure under investigation.

This thesis will focus on the use of an array of actuators. Piezoelectric Wafer Active Sensors(PWAS) are bonded to an aluminum plate to generate radially propagating Lamb waves. Aprogram is written to simulate the Lamb wave propagation. This program is used to show theareas of constructive interference from the array.

It was tried to make a numerical simulation of the Lamb wave propagation. Due to softwareconstraints, this was not succesfull. Radial propagation is yet possible but the propagation speedis not in agreement with the Lamb wave propagation speed.

Experiments were used to optimise the program written. Two control sensors were adjusted tothe plate and it was shown that the signal was stronger in the control sensor in the area ofconstructive interference.

Keywords

array, Lamb waves, PWAS, constructive interference

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Resumo

Structural Health Monitoring (SHM) e um domınio de investigacao que tem crescido nos ultimosanos.SHM envolve o desenvolvimento de sistemas integrados destinados a monitorizacao contınuada condicao de uma estrutura, tendo em vista garantir a necessaria integridade estrutural. Nodomınio aeroespacial, o fim visado com SHM e a garantia da necessaria seguranca com custosmınimos. Para atingir este objectivo, pretende-se reduzir os perıodos de imobilizacao de umaaeronave, necessarios para verificar a sua condicao estrutural atraves da realizacao de ensaiosnao-destrutivos, utilizando sistemas embebidos durante os perıodos normais de imobilizacao daaeronave ou com esta mesmo em voo.

A existencia de defeitos estruturais num componente implica alteracoes locais nas suas pro-priedades. As ondas de Lamb podem ser utilizadas na deteccao destas alteracoes, atraves damedicao de variacoes na sua propagacao, permitindo a identificacao dos defeitos e logo assegu-rando a necessaria integridade estrutural do componente.

Esta tese foca aspectos do estudo e aplicacao de um agregado de atuadores. Piezoelectric WaferActive Sensors (PWAS) quando colados numa placa produzem ondas de Lamb que se propagamradialmente. Foi implementado um programa que modela e simula a propagacao destas ondasde Lamb. Este programa foi utilizado no estudo da propagacao das ondas de Lamb geradas porum agregado de actuadores, permitindo identificar as zonas onde ocorre a resultante interferenciaconstrutiva.

Procurou-se validar os resultados obtidos atraves da simulacao numerica da propagacao de ondasde lamb, utilizando um programa de elemntos finitos (ANSYS). Devido a varias restricoes desteprograma, esta validacao nao foi totalmente conseguida. Foi possıvel a simulacao da propagacaoradial mas a resultante velocidade de propagacao nao e coerente.

Procurou-se entao validar o programa desenvolvido atraves da implementacao e utilizacao demontagens experimentais. Os resultados experimentais obtidos sao corenetes com os resultadosprevistos pelo programa desenvolvido.

Palavras-chave

agregado de actuadores, Lamb waves, PWAS, interferencia construtiva

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Samenvatting

Dit werk onderzoekt de mogelijkheden van phased arrays in Structural Health Monitoring (SHM).Er werd een programma geschreven om te simuleren hoe de signalen zich voortplanten. Met ditprogramma werd aangetoond dat signalen afkomstig van een array van actuatoren interfererenen dat er zones van constructieve interferentie ontstaan. Het is mogelijk deze zones te sturen inverschillende richtingen door de signalen niet allemaal tegelijk te zenden. Het programma werdgeverifieerd met experimentele resultaten. Hierbij werd de invloed van de frequentie en van hetverzonden signaal ook onderzocht.

0.1 Inleiding

Structural Health Monitoring (SHM) verwijst naar het concept om de performantie van een struc-tuur te onderzoeken terwijl de structuur zijn normale activiteit uitoefent. Het uiteindelijke doelvan SHM is de betrouwbaarheid te verhogen, de veiligheid te garanderen, het design zo lichtmogelijk te houden en de onderhoudskosten te beperken voor allerlei verschillende structuren.Ultrasoon onderzoek is een methode die vaak gebruikt wordt in SHM. Het huidige ultrasoon on-derzoek van dunne structuren is echter zeer tijdrovend. Een manier om de efficientie te verhogenis het gebruik van guided waves in plaats van de conventionele drukgolven. Guided waves kunnenzich relatief ver voortplanten in een structuur zonder veel demping. Ze hebben ook het voordeeldat ze een grote oppervlakte kunnen onderzoeken met weinig sensoren. Guided Lamb wavesbrachten nieuwe mogelijkheden voor rendabel schade onderzoek in structuren van vliegtuigen.

Recentelijk onderzochten verschillende onderzoeksgroepen de generatie van Lamb waves metPiezoelectric Wafer Active Sensors (PWAS). PWAS zijn goedkope sensoren die de structuurminimaal beınvloeden en die bovenop de bestaande structuren of tussen de lagen van composiet-materialen kunnen bevestigd worden. PWAS koppelen hun beweging in het vlak met de Lambwave beweging op het materiaal oppervlak. De beweging in het vlak wordt veroorzaakt door eenoscillerende spanning met behulp van het piezo-elektrisch effect. Een probleem van Lamb wavesis dat ze dispersief zijn: hun snelheid verandert met de frequentie van het verzonden signaal(figuur 1). Dit werk onderzoekt signalen met lagere frequentie omdat dan enkel de S0 and A0

mode geactiveerd wordt. Bij deze lage frequenties is er een groot verschil tussen de snelheid vanbeide modes zodat de verschillende golfeenheden kunnen onderscheiden worden.

Bij phased array onderzoek combineren de signalen afkomstig van de verschillende actuatorenzodanig dat een gebied van constructieve interferentie ontstaat. Door specifieke delays te geven

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Figure 1: Dispersief karakter van Lamb waves

aan deze signalen, kan dit gebied gestuurd worden. Als de tussenruimte tussen de verschillendeactuatoren te groot is ontstaan er meerdere gebieden met constructieve interferentie. Dit ishet ongewenste fenomeen van grating lobes. De gemakkelijkste manier om deze grating lobes teminimaliseren is door de tussenruimte tussen de sensoren kleiner te houden dan de helft van dekleinste golflengte die aanwezig is.

0.2 Beschrijving van het geschreven programma

Een programma werd geschreven in MATLAB. Om berekeningen met MATLAB uit te voerenis het enkel mogelijk om te werken met discrete eenheden. Daarom werd er een rij gecreeerd,genoemd time, om de tijd te simuleren. Het programma definieert een drie dimensionale matrix:K x K x t met K het aantal onderverdelingen in de X en Y richting op een vierkante plaat in hetXY-vlak en met t het aantal tijdsintervallen. De oorsprong van het gebruikte assenstelsel is inde linkerbenedenhoek van de plaat verondersteld. Om de matrix te linken aan de werkelijkheidwerd een parameter delta ingevoerd. De tussenruimte tussen twee punten in de XY-grid is gelijkaan delta mm. De propagatie van signaal 1 werd gesimuleerd waarbij A de amplitude is en f defrequentie.

A sin(2πf · t) · sin(2πf/10 · t) (1)

0.2.1 Radiale propagatie

De actuator wordt verondersteld in het punt [X;Y]. De snelheid waarmee het signaal propageertis geweten voor een welbepaalde frequentie. Met deze snelheid (vel) wordt berekend wanneer hetsignaal arriveert in een gegeven punt P [x;y]. Als de actuele tijd groter is dan dit moment B ishet punt P onder de invloed van het signaal en wordt de amplitude van het signaal in P berekend

door middel van een welbepaalde delay toe te passen op het originele signaal A(t). De radialepropagatie is geıllustreerd met figuur 2.

R =√

(x−X)2 + (y − Y )2

B = R ∗ delta ∗ 10−3/cif B ≤ time(t)

D = round(B/deltaT ime)F (y, x, t) = A(t−D)

end

Figure 2: Radiale propagatie van het signaal: (a) zonder reflecties, (b) met reflecties

0.2.2 Eerste reflecties

Wiskundig zijn Lamb waves cirkels met center in de actuator, die groeien met de tijd. Als eendeel van die cirkel bij de rand aankomt, wordt hij symmetrisch gereflecteerd in de tegengestelderichting. Voor elke rand wordt de tijd berekend die het signaal nodig heeft om tot bij de randte komen. Als de actuele tijd groter is dan deze tijd worden de reflecties berekend. Racc is deafstand die het signaal aflegde bij de actuele tijd. Vervolgend is het gebied onder invloed van dereflectie berekend. Voor elk punt in dit gebied wordt dan de amplitude van het signaal berekenddoor de gepaste delay toe te passen op het originele signaal. Een deel van de code voor reflectiesvan de linkerzijde is hieronder weergegeven.

Dleft = X;T left = Dleft/vel ∗ delta ∗ 10−3;Racc = time(t) ∗ vel/(delta ∗ 10−3);if time(t) > Tleft

H = sqrt(Racc2 −Dleft2);yMin = round(Y −H);yMax = round(Y +H);

for y = yMin : yMaxDist = round(abs(X − sqrt(Racc2 − (y − Y )2)));for x = 1 : Dist

R = sqrt((Dleft+ x)2 + (Y − y)2);B = R ∗ delta ∗ 10( − 3)/vel;D = round(B/deltaT ime);Fleft = A(t−D) ∗ exp(−εR);

endend

end

0.2.3 Toegepaste delays

Om de samenwerking van verschillende actuatoren te simuleren worden de directe en gereflecteerdesignalen van alle actuators berekend en bij elkaar opgeteld. Een uniforme lineaire array van Mactuatoren (PWAS) met een tussenruimte d is verondersteld. Om de delays te vinden die moetentoegepast worden opdat het gebied met constructieve interferentie in de richting φ constructieveinterferentie vertoont, wordt ervan uitgegaan dat de signalen min of meer parallel aankomen ineen bepaald punt P op een afstand r van de array die veel groter is dan d. Giurgiutiu berekendedat de delays gelijk moeten zijn aan:

∆m(φ) = m(d cos(φ)/c (2)

met m het number van de actuator en met c de snelheid van de Lamb waves.

Figure 3: Uniforme lineare array van M actuators met tussenruimte d

0.2.4 Enkele resultaten

Een array van zeven actuatoren werd gesimuleerd. De ruimte tussen de verschillende actuatorenwerd gevarieerd en de invloed hiervan werd onderzocht. In figuur 4 kan gezien worden dat hetgebied met constructieve interferentie het best gedefinieerd is met een tussenruimte van 20 mm.Met een tussenruimte van 40 mm zijn er grating lobes aanwezig.

Vervolgens werd onderzocht of de delays de richting van constructieve interferentie goed definieren.In figuur 5 kan gezien worden dat dit zo is. Als de hoek echter te klein is of te dicht bij 180°komt, is het gebied van constructieve interferentie niet meer zo nauwkeurig bepaald.

Figure 4: Variatie van de tussenruimte met zeven actuatoren

Figure 5: Variatie van de richting van constructieve interferentie

0.3 Experimentele setup

De experimentele setup bestaat uit een aluminium plaat waarop piezoelectrische transductoren(PWAS)bevestigd werden. Via kabels, een NI Expresscard-8360 en een Data Acquisition Unit NI PXI-1333met 9 uitgangen en 4 ingangen, wordt informatie uitgewisseld tussen een laptop en de transduc-toren. Een oscilloscoop en een functiegenerator zijn gesimuleerd in een LABVIEW omgeving.

De aluminium plaat die onderzocht werd is een vierkante plaat van 1, 5 m x 1, 5 m x 2 mm.De experimenten maakten gebruik van twee zulke platen. Een van hen was een beschadigdeplaat met drie transductoren in een netwerk configuratie. Deze plaat was op twee plaatsenbeschadigd. De eerste snede (20 mm x 1 mm) was parallel met de onderrand van de plaat en detweede snede (40 mm x 1 mm) was loodrecht op de richting transductor 1 - transductor 2. Deandere plaat was niet beschadigd en werd uitgerust met een array van vier transductoren en tweecontroletransductoren. De coordinaten van de transductoren kunnen teruggevonden worden intable 1. Hierbij werd de oorsprong van het assenstelsel vastgelegd in de linkerbenedenhoek vande plaat.

Network Arrayx (mm) y (mm) x (mm) y (mm) x (mm) y (mm)

1 1125 750 1 712 45 4 787 452 750 375 2 737 45 C1 750 7503 375 1125 3 762 45 C2 300 588

Table 1: Coordinaten van de transducers

0.4 Invloed van de frequentie

De eerste serie experimenten werd uitgevoerd op de beschadigde plaat met een netwerk vantransductoren. Het signaal dat werd gegeven aan de actuatoren is:

a(t) = sin(ωAt) · sin(ωA10t) (3)

met ωA = 2πf kHz. Dit signaal werd toegepast gedurende 5/f s.

Omdat Lamb waves dispersief zijn, varieert de snelheid met de frequentie. Voor elke frequentiekan de snelheid van de S0 en A0 Lamb wave gevonden worden in de dispersie grafiek (figuur 1). Deafstand tussen de transductoren is ook geweten dus kan berekend worden wanneer het signaal ineen bepaalde sensor aankomt. Als het signaal een rand van de plaat bereikt, is het veronderstelddat het signaal symmetrisch gereflecteerd wordt in de tegengestelde richting. Zo kan de afstandberekend worden die een bepaalde golfeenheid aflegt om in een sensor te arriveren na reflectie(tabel 2). De golfeenheden die arriveren in sensor i van actuator j leggen precies dezelfde afstandaf als de golfeenheden die arriveren in sensor j van actuator i. Nu kunnen de tijdstippen berekendworden wanneer de golfeenheden arriveren in een bepaalde sensor. Het signaal duurt 5/f s dus

Figure 6: De onderzochte platen: (a) Beschadigd, met netwerk van transductoren, (b)Onbeschadigd, met array van vier transductoren en twee controletransductoren

daarmee is ook geweten wanneer de golfeenheid de sensor verlaat. Met deze informatie kunnen deverkregen signalen van de experimenten geınterpreteerd worden. De verschillende golfeenhedenzijn aangeduid in figuur 7 en 8. S0 en A0 beduiden het directe signaal en wanneer er een lettertussen haakjes volgt, beduidt dit een reflectie. Hierbij staan s, n, e en w respectievelijk voor dereflectie van de onderrand, bovenrand, linkerrand en rechterrand. De verschillende golfeenhedenzijn het beste te herkennen met een frequentie tussen 100 kHz en 200 kHz.

Actuator sensor Direct Reflectie s Reflectie n Reflectie e Reflectie w1 2 530,33 1185,85 1912,13 1185,85 1912,131 3 838,53 2019,44 1352,08 1546,16 1546,162 1 530,33 1185,85 1912,13 1185,85 1912,132 3 838,53 1546,16 1546,16 2019,44 1352,083 1 838,53 2019,44 1352,08 1546,16 1546,163 2 838,53 1546,16 1546,16 2019,44 1352,08

Table 2: Afgelegde afstand van de signalen van actuator i tot sensor j

Vervolgens werd een studie uitgevoerd om de amplitude van de directe S0 en A0 golfeenhedente bepalen. Tussen de aankomst- en vertrektijd van de golfeenheden bereikt het signaal immerseen maximum en naar deze maxima werd gezocht. Helaas kon er geen data gevonden wordenvoor de directe A0 golfeenheden bij lage frequentie omdat er overlap is met de reflecties van deS0 golfeenheden. Figuur 9 geeft de resultaten van deze studie. De S0 en A0 amplitude vertoneneen gelijkaardig patroon maar de A0 amplitude is lager. De demping van het signaal tussen deS0 amplitude bij 0, 533 m en bij 0, 839 m kan ook gezien worden.

Figure 7: Invloed van de frequentie op de verkregen signalen in sensor 1 met actuator 2

Figure 8: Invloed van de frequentie op de verkregen signalen in sensor 3 met actuator 2

0.4.1 Dempingfunctie

In dit onderdeel zal getracht worden een goede dempingfunctie te definieren voor een signaal van200 kHz. Zoals gezien kan worden in 9 varieert de amplitude van het signaal met frequentie enmet afstand tot de actuator. De functie die hier gezocht wordt, is enkel afhankelijk van de afstandtot de actuator en is gebaseerd op de waarden in tabel 3.

Figure 9: Variatie van de amplitude van de S0 en A0 signalen met frequentie

Afstand (m) S0 amplitude A0 amplitude0 1 1

0,53033 0,08786 0,0320180,83853 0,057840751,18585 0,0463081,35208 0,0336665

Table 3: Amplitude van het signaal in functie van de afstand tot de actuator

De volgende dempingfuncties werden geprobeerd:

� (R/1000)2

� (R/1000)5/2

� (R/1000)3

� (R/1000)(10/3)

� een veeltermfunctie van graad 6 door de punten, gegenereerd door Excel

R is de radiale afstand (in m) tot de actuator. De veeltermfunctie werd verworpen omdat zeniet constant dalend is. De conclusie van deze studie was dat de dempingfunctie (R/1000)10/3

het beste was voor de S0 mode en (R/1000)2 voor de A0 mode. Om dezelfde amplitudes als inde signalen verkregen uit de experimenten te bekomen, moeten de dempingfuncties nog gedeeldworden door dertig. Dit is een vermenigvuldigingsfactor die gebruikt werd bij de oscilloscoop.De resultaten met actuator 2 zijn weergegeven in figuur 10.

Figure 10: Finale vergelijking: (a) sensor 1 - actuator 2, (b) sensor 3 - actuator 2

0.4.2 Resonantiefrequentie

De amplitude functies in figuur 9 bereiken een maximum bij een amplitude van ongeveer 150 kHz.Dit suggereert dat deze frequentie de resonantiefrequentie is van het geheel. Om dit nader te on-derzoeken, werd er een puls aan de actuator gegeven. De power spectra van deze experimentenvertoonden allen een maximum rond de 150 kHz. Een van deze power spectra is weergegevenin figuur 11. De exacte frequenties waarbij het maximum optreedt, werden opgezocht en zijnweergegeven in tabel 4. Het gemiddelde van al deze frequenties is 143,4 kHz en dit wordtbeschouwd als de resonantiefrequentie van het systeem.

Figure 11: Power spectrum

Test Frequency (kHz)1 1462 1443 1544 1325 136,86 147,6

Average 143,4

Table 4: Resonantiefrequentie

0.5 Resultaten met twee actuatoren

Op de beschadigde plaat met een netwerk van transducers werden twee transducers gebruikt alsactuator. Het signaal in de derde transducer, die gebruikt werd als een sensor, wordt verondersteldde som te zijn van de signalen in de derde transducer met elk van de twee actuators afzonderlijk.Resultaten met een frequentie van 150 kHz zijn weergegeven in figure 12. Het grootste verschiltussen het experimenteel verkregen signaal en de som van de twee signaals is 5%.

Figure 12: Resulten met twee actuatoren, signaal in sensor 2: (a) experimentele resultaten, (b)geprogrammeerde resultaten

0.6 Constructieve interferentie met een array van vier

actuatoren

Een simulatie werd uitgevoerd om te weten hoe het signaal afkomstig van een array van vieractuatoren zonder delays, propageert. Deze simulatie toonde dat het gebied met constructieveinterferentie aan de voorzijde van de array ligt. In dit gebied situeert zich C1. Bijgevolg wordter in C1 een signaal met grotere amplitude verwacht dan in C2. De aandacht werd toegespitst opde aankomst van het directe S0 signaal omdat dit eerst arriveert in de sensors en omdat er geenoverlap is met reflecties. In figuur 13 kan gezien worden dat een array van twee actuators reedseen beetje constructieve interferentie heeft. Met een array van vier actuatoren wordt echter eengrotere constructieve interferentie verkregen.

Figure 13: Constructieve interferentie met een array : (a) signalen in C1, (b) signalen in C2

0.7 Verschillende toegepaste signalen

Sommige andere signalen waren nu aan de actuatoren gegeven en de invloed hiervan werdbestudeerd. Er werd een naam gegeven aan deze signalen om de volgende bespreking te vereen-voudigen:

� signaal 1: sin(2πft) · sin(2πf10 t)

� signaal 2: sin(2πft) · 12(1− cos(2πf

5 t))

� signaal 3: sin(2πft) · 12(1− cos(2πf

5 t))2

� signaal 4: sin(2πft) · 12(1− cos(2πf

5 t))1/2

Voor elke van deze signalen werd het power spectrum berekend (figuur 15). Enerzijds kan menin figuur 14 zien dat signaal 3 een trager begin en einde heeft. Anderzijds toont figuur 15 dat

Figure 14: Bestudeerde signalen: (a) signaal 1, (b) signaal 2, (c) signaal 3, (d) signaal 4

signaal 3 het laagste power spectrum heeft. Signaal 1 en 4 zijn zeer gelijkend. Ook hun powerspectrum is in goede overeenkomst en is het grootste van alle signalen in deze studie. Signaal 2heeft niets speciaals en er zal geen aandacht meer aan besteed worden.

Figure 15: Power spectrum van de verschillende signalen

Tot hiertoe is het nog niet duidelijk welk signaal het beste resultaat geeft. Enkele experimentenwerden uitgevoerd op de niet-beschadigde plaat met de array om meer duidelijkheid te creeren.De signalen werden getest bij een frequentie van 80 kHz, 140 kHz en 200 kHz. De experimententoonden (figuur 16) dat het signaal veel meer ruis heeft met een frequentie van 80 kHz. Deverschillende signalen die aankomen in C1 met een frequentie van 200 kHz zijn een beetje betergedefinieerd dan degene met een frequentie van 140 kHz. De amplitude is echter groter met een

signaal van 140 kHz. Dit is omdat 140 kHz dicht bij de resonantiefrequentie van het systeemligt.

Een vermenigvuldigingsfactor amplitude S0 C1amplitude S0 C2 werd vervolgens bestudeerd voor signaal 1, signaal

3 and signaal 4 met frequenties 140 kHz en 200 kHz. De resultaten zijn weergegeven in tabel 5.Deze factor is het grootst voor signaal 3 bij 200 kHz echter de verschillen zijn klein.

Uiteindelijk besluiten we dat signaal 3 met 140 kHz de beste resultaten geeft. De ontvangensignalen hebben een grote amplitude zodat ze makkelijk te distancieren zijn van ruis. Bovendienis er een goede constructieve interferentie aangezien de vermenigvuldigingsfactor groot is.

0.8 Poging tot sturen van het signaal

Met de gebruikte apparatuur was het niet mogelijk om delays aan de signalen te geven. Omhet signaal te sturen werd de invloed van een omkering van de polarisatie van de transducersbestudeerd. In figuur 17 kan men de voorspelde propagatie van de signalen zien. Zoals eerdergezegd gaat het signaal rechtdoor als de vier actuators dezelfde polarisatie hebben. Als er aanA1 en A4 een signaal aangelegd wordt en ze hebben een verschillende polarisatie, dan zijn degebieden met constructieve interferentie niet zo goed gedefinieerd omdat de tussenruimte tussendeze twee actuatoren tamelijk groot is. Als hetzelfde gedaan wordt maar met A2 en A3 is hetgebied met constructieve interferentie tamelijk groot. Het beste resultaat wordt verkregen als eraan de vier actuatoren een signaal aangelegd wordt en als A1 en A2 een tegengestelde polarisatiehebben dan A3 en A4. Daarom werden de connecties van A3 en A4 op de plaat omgekeerd.

De experimenteel verkregen signalen met signaal 3 bij een frequentie van 200 kHz zijn weergegevenin figuur 18. De S0 mode arriveert in de sensoren na 130, 6 µs en verlaat hen 25 µs later. Zoalseerder gezegd is er een sterke constructieve interferentie in C1 met de vier actuatoren met zelfdepolarisatie. Als de polarisatie van A3 en A4 wordt omgedraaid, kan men vaststellen dat het signaalin C2 niet noemenswaardig sterker is dan het signaal in C1. Dit komt doordat C2 niet exact inhet gebied met constructieve interferentie ligt. De constructieve interferentie in C2 kan gezienworden in de resultaten met enkel A1 en A4 en met enkel A2 en A3, telkens met verschillendepolarisatie. In deze gevallen is C2 in het gebied van constructieve interferentie gepositioneerd.

140 kHz 200 kHzsignal 1 6,362 6,451signal 3 6,619 6,738signal 4 6,362 6,547

Table 5: Vermenigvuldigingsfactor

Figure 16: Ontvangen signalen met signaal 3: (a) 80 kHz in C1, (b) 80 kHz in C2, (c) 140 kHzin C1, (d) 140 kHz in C2, (e) 200 kHz in C1, (f) 200 kHz in C2

Figure 17: Invloed van de polarisatie: (a) vier actuatoren, zelfde polarisatie, (b) A1 en A4,verschillende polarisatie, (c) A2 en A3, verschillende polarisatie, (d) A1 en A2 mettegengestelde polarisatie dan A3 en A4

Figure 18: Experimentele resultaten: (a) signalen in C1, (b) signalen in C2

Studies on phased array actuators for aircraftStructural Healt Monitoring

Veerle Van Doorsselaere

Supervisor(s): Prof. A. Suleman, prof. A. Fonseca, prof. J. Degrieck

Abstract— This article describes a program to simulate the Lamb wavepropagation. With this program, the areas with constructive interferencefrom an array of actuators are shown. This is experimentally verified. Theinfluence of frequency and actuation signal is studied.

Keywords—array, Lamb waves, PWAS, constructive interference

I. INTRODUCTION

Structural Health Monitoring (SHM) refers to the broad-concept of assessing the ongoing, in-service performance ofstructures using a variety of measurement techniques. The ul-timate goal of SHM is to increase reliability, improve safety,enable light-weight design and reduce maintenance costs for allkinds of structures. Ultrasonic testing is one method used inSHM. Current ultrasonic inspection of thin wall structures isa time consuming operation. One method to increase the effi-ciency is to use guided waves instead of the conventional pres-sure waves. Guided waves propagate along the mid-surface ofthin-wall plates and shallow shells. They can travel at relativelylarge distances with very little amplitude loss and offer the ad-vantage of large-area coverage with a minimum of installed sen-sors. Guided Lamb waves have opened new opportunities forcost-effective detection of damage in aircraft structures.

In recent years, several investigators have explored the gen-eration of Lamb waves with piezoelectric wafer active sensors(PWAS). PWAS are inexpensive, non-intrusive, un-obtrusiveand minimally invasive devices that can be surface-mounted onexisting structures or inserted between the layers of lap joints orinside composite materials. PWAS couple their in-plane motion,excited by the applied oscillatory voltage through the piezoelec-tric effect, with the Lamb waves particle motion on the materialsurface. One problem of Lamb waves is that they are dispersive,i.e., their velocity changes with the frequency of the applied sig-nal (figure 1). This paper will investigate signals with lowerfrequencies in order to only excite the S0 and A0 modes. At thislow frequencies, the velocity of both modes is different so thedifferent wave packages can be seen separately.

In phased array testing, the signals from the different actua-tors combine to form an area of constructive interference. Byapplying specific phase delays to the actuators, the area of con-structive interference can be steered. By changing the patternof the delays, more steering possibilities occur. When the in-terspace between the different actuators is too big, unwantedareas with constructive interference appear. This phenomenonis called grating lobes. The simplest way to minimize gratinglobes in a given application is to use a transducer interspacingsmaller than half the smallest wavelength under consideration.

Fig. 1. Dispersive nature of Lamb waves

II. DESCRIPTION OF PROGRAM

A program was written in MATLAB. In MATLAB, it is onlypossible to work with discrete arrays. Therefore a time array iscreated, called time. The program defines a three dimensionalarray: K x K x t with K the number of divisions on the platein the X and Y direction and t the number of time intervals. Theorigin of the plate is considered to be in the down left cornerof the plate. To make the link with the real plate of K x K,a paramater delta is introduced. The interspacing between twopoints in the XY-grid is equal to delta mm. Signal 1 is used inthe simulations.

A sin(2πf · t) · sin(2πf/10 · t) (1)

A. Radial propagation

The wave is actuated at point [X(a), Y (a)]. For a given fre-quency, the group velocity of the Lamb waves is known. Withthis velocity (vel), the moment the wave arrives in a certain pointP is calculated (B). If the actual time is later than this moment,the point is under the influece of the wave and the delay the sig-nal has in P is calculated (D). Now, the amplitude of the signalin P is calculated by applying this delay to the signal of the ac-tuator A(t). The radial propagation of the signal can be seen infigure 3.

B. Primary reflections

Mathematically Lamb waves are circles with center in the ac-tuator growing with time. When a part of that circle arrives to aboundary, it is reflected symmetrically in the opposite direction.

R=sqrt((x-X(a))ˆ2+(y-Y(a))ˆ2);B=R*DELTA*10ˆ(-3)/vel;if time(t)>=BD=round(B/deltaTime);ampl=A(t-D);

end

Fig. 2. Programmed radial wave propagation

Fig. 3. Radial propagation of the signal: (a) without reflections, (b) with reflec-tions

For the left boundary reflection the time the signal needs to ar-rive to the left boundary is calculated (Tleft). If the actual time isbigger than this time, the reflections are calculated. Racc is thedistance the wave travelled after the actual time. The area underinfluence is then defined: the Y-component varies from Ymin toYmax and the X-component varies from 1 to Dist, where Distis defined by using the equation of a circle. For each point inthis area, the amplitude of the signal is calculated by applyingthe proper delay to the actuated signal. In a similar way, theprimary reflections from the upper, down and right border areobtained.

Dleft=x;Tleft=Dleft/c*delta*10ˆ{-3};Racc=tijd(t)*c/(delta*10ˆ(-3));if tijd(t)>TleftH=sqrt(Raccˆ2-Dleftˆ2);yMin=round(Y-H);yMax=round(Y+H);for y=yMin:yMaxDist=round(abs(X-sqrt(Raccˆ2-(y-Y)ˆ2)));for x=1:DistR=sqrt((Dleft+x)ˆ2+(Y-y)ˆ2);B=R*delta*10ˆ(-3)/c;D=round(B/deltaTime);Fleft=A(t-D);

endend

end

Fig. 4. Programmed primary reflections

C. Applied delays

When simulating interference from different actuators, the di-rect and reflected signals are calculated for each actuator andadded together. To define the delays for steering, a uniform lin-ear array of M actuators (PWAS) with an interspacing of dis-tance d is assumed. The area with constructive interference needto be steered to a direction of angle φ. This can be calculatedusing a parallel ray approach if the distance d is assumed muchsmaller than the distance r to a generic, far-distance point P. Ac-cording to [2], the delays are equal to

∆m(φ) = m(d cos(φ)/c (2)

with m the number of the transducer and c the group velocity ofthe Lamb waves.

Fig. 5. Uniform linear array of M omni-directional sensors (PWAS) spaced atpitch d

D. Guided User Interface

A Guided User Interface, GUI, was developed in order tostudy the influence of the different parameters more easily. ThisGUI consists of several blocks, each defining a particular partof the Lamb wave propagation. The settings are for a plate of1, 5 m x 1, 5 m x 2 mm. The different blocks will now be de-scribed:• Hanning window input - In this block, one has to define theamplitude A and two frequencies: f1 and f2. This two parame-ters define the Hanning window as follows:

a(t) = A · sin(2π f1 · t) · sin(2π f2 · t) (3)

• Lamb wave propagation - The propagation speed of the sig-nal is equal to the group velocity. The group velocity depends onthe Lamb wave mode and of the frequency-thickness product.This GUI simulates the S0 and A0 Lamb wave modes. Somefrequency-thickness products are predefined.• Damping - The damping coefficient ε and the damping func-tion can be varied.• Actuators - The number of actuators can be chosen and foreach actuator the position needs to be told to the program. Itis also possible to work with different scales. The interspacebetween two point in the grid is equal to delta mm. Dependingon delta, the number of elements in the X and Y-direction goesfrom 1 to K.• Phase delays - The phase delays can be calculated by defininga steering angle or can be manually defined.• Plots - Three plots will be generated during the program ex-ecution. Each of these plots can be defined in three ways. The

first way is to generate the grid and define a colourmap of theamplitudes in each point at a certain time. Another way is bygiving the time signal in one actuator and the last way is by giv-ing the time signal in a certain point under interest.

III. EXPERIMENTAL SETUP

The experimental setup consists of an aluminum plate andsome piezoelectric wafers. By use of cables, a NI Expresscard-8360 and a Data Acquisition Unit NI PXI-1333 with 9 outputsand 4 inputs, information is passed between a laptop and thetransducers. A oscilloscope and a function generator are simu-lated in LABVIEW. The oscilloscope is a NI PXI-5105 and thefunction generator is a NI PXI-5421. Everything together sim-ulates a PCI eXtensions for Instrumentation, PXI, environment.PXI combines PCI electrical bus features with the rugged mod-ular Eurocard packaging of CompactPCI, and then adds special-ized synchronization buses and key software features. [4]

The aluminum plate under investigation is a square plate of1, 5 m x 1, 5 m and 2 mm thickness. The experiments madeuse of two plates. One is a damaged one with three sensorsin a network configuration. This plate has two cuts: one of size20mmx 1mm and parallel to the northern and southern bound-ary (first cut) and the other of size 40 mm x 1 mm and perpen-dicular to the direction transducer 1 - transducer 2. The secondplate is a non-damaged plate. This plate is instrumented withan array of four transducers and two control transducers. Theorigin of the plates is considered to be in the down left cornerand the plate is considered to be in the XY-plane with the Z-ascoming out of the plate. The coordinates of the transducers canbe found in table I and table II.

TABLE ICOORDINATES OF THE TRANSDUCERS IN THE NETWORK CONFIGURATION

Networkx (mm) y (mm)

1 1125 7502 750 3753 375 1125

TABLE IICOORDINATES OF THE TRANSDUCERS IN THE ARRAY CONFIGURATION

Arrayx (mm) y (mm) x (mm) y (mm)

1 712 45 4 787 452 737 45 C1 750 7503 762 45 C2 300 588

IV. VARIATION OF FREQUENCY

A study of the frequency influence was done. This study wasperformed on the damaged plate and used actuator 2 and sensor1 and 3. The arrival time of the different wave packages can becalculated as the wave speed and distance is known. With thisinformation, the signals obtained in the sensors can be under-stood. In the figures below, the wave packages are indicated. S0

Fig. 7. Plates under investigation: (a) Damaged plate with network of transduc-ers, (b) Non-damaged plate with array of four transducers and two controltransducers

and A0 stand for the arrival of the direct wave, respectively S0

and A0. If there is a letter adjusted between brackets, it meansthe arrival of a primary reflection. The letters used are s, n, eand w and they are standing for respectively south, north, eastand west. It can be seen in the figures below that the wave pack-ages are best visible with a frequency between 100 kHz and200 kHz.

Fig. 8. Influence of frequency on obtained signal in sensor 1 with actuator 2

Fig. 9. Influence of frequency on obtained signal in sensor 3 with actuator 2

As the different wave packages can be distinguished, the am-plitude of this wave packages can be found. It can be seen infigure 10 that the A0 amplitude follows a similar pattern as theS0 amplitude but at a lower amplitude.

Fig. 6. Radial propagation of the signal

Fig. 10. Variation of Lamb wave amplitude with frequency: (a) with actuator 1,(b) with actuator 2

A. Natural frequency

It can be seen in figure 10 that the amplitude functions reacha maximum around 150 kHz. This suggests the existence of anatural frequency there. To verify this, some pulses were appliedto the actuator and the power spectra of the received signals wereinvestigated. The power spectra looks like 11. The frequencieswhere the maximum occurs, are noted. The average of them is143,4 kHz and this is considered as the natural frequency of thesystem.

B. Damping function

To avoid the excitation of a resonance signal, experimentswere done with a signal of 200 kHz. As can be seen in fig-

Fig. 11. Power spectrum of the signal in sensor C1

ure 10, the amplitude of the signal varies with frequency andwith distance. In this part, an appropriate damping function willbe defined for a signal of 200 kHz. This function is only depen-dent of the distance from the actuator. The following dampingfunctions were tried:• (R/1000)2

• (R/1000)5/2

• (R/1000)3

• (R/1000)10/3

• a polynomial trendline (degree 6) through the keypoints, givenby ExcelR is the radial distance (in m) from the actuator. In the end, itwas concluded that a damping function of (R/1000)10/3 wasthe best for the S0 propagation and (R/1000)2 for the A0 prop-

Fig. 12. Final comparison with adapted damping function: (a) sensor 1 - actua-tor 2, (b) sensor 3 - actuator 2

agation. To obtain the right amplitude, the damping function hasto be divided by thirty. This is the multiplication factor used forthe oscilloscope. Results with actuator 2 can be seen in figure12.

V. INTERFERENCE WITH TWO ACTUATORS

On the damaged plate with a network of transducers, twotransducers were used as actuator. The signal in the third trans-ducer, used as a sensor, is supposed to be the sum of the sig-nal received there with each of the actuators separately. Resultswith a frequency of 150 kHz can be seen in figure 13. It wascalculated that the biggest difference between the experimentalobtained result and the sum of the two signals is about 5%.

Fig. 13. Results with two actuators, signals taken in sensor 2: (a) experimentalresults, (b) programmed results

VI. CONSTRUCTIVE INTERFERENCE WITH THE ARRAY

Next, an array of four actuators was implemented on the non-damaged plate and tested by using two control sensors. A sim-ulation was done of the propagation of the signal with four ac-tuators. This simulation showed (figure 14) that the area with

constructive interference is in front of the array. Because C1 islocated in front of the array, a stronger signal should be encoun-tered in C1 then in C2. Focus for the constructive interference ispayed to the direct S0 wave package which arrives at first in thesensors and has no problems with overlap with primary reflec-tions. In figure 15, it can be seen that an array of two actuatorsalready has some constructive interference. With an array offour actuators, the constructive interference is even bigger.

Fig. 14. Programmed propagation of the signal: (a) 0,00007 s, (b) 0,0001 s

VII. TESTING OF DIFFERENT ACTUATION SIGNALS

The influence of some other signals was studied. These sig-nals are given some names to simplify the following discussion:• signal 1: sin(2πft) · sin( 2πf

10 t)• signal 2: sin(2πft) · 1

2 (1 − cos( 2πf5 t))

• signal 3: sin(2πft) · 12 (1 − cos( 2πf

5 t))2

• signal 4: sin(2πft) · 12 (1 − cos( 2πf

5 t))1/2

For each of these signals the power spectrum is calculated(figure 17). In the previous described experiments, signal 1 isused. By looking at the signals, signal 3 seems to be a bettersignal because it has a slower beginning and ending. Neverthe-less it has the lowest power response. Signal 1 and signal 4 lookvery similar. Also their power spectrum is in good agreement.Signal 2 has nothing special and no more attention will be payedto it.

Up till now it is not clear which signal will give the best re-sults. Some experiments on the non-damaged plate were doneto give more information. These experiments were done with afrequency of 80 kHz, 140 kHz and 200 kHz and with the fouractuators of the array actuated. The experiments showed (figure18) that the signal in C2 has a lot of noise when applying a sig-nal of 80kHz to the actuators. The wave packages received inC1 with an actuation signal of 200 kHz are a little bit better de-fined then the one received with an actuation signal of 140 kHzalthough the amplitude of the signal is bigger with an actuationsignal of 140 kHz. This because 140 kHz is about the naturalfrequency of the system.

The multiplication factor amplitude S0 C1amplitude S0 C2 is now studied for

signal 1, signal 3 and signal 4 with frequencies of 140 kHz and200 kHz. Results are noted down in table III. The multiplica-tion factor is the biggest for signal 3. It should be mentionedthat the differences are not so big.

Fig. 18. Received signals with signal 3: (a) 80 kHz in C1, (b) 80 kHz in C2, (c) 140 kHz in C1, (d) 140 kHz in C2, (e) 200 kHz in C1, (f) 200 kHz in C2

TABLE IIIMULTIPLICATION FACTOR

140 kHz 200 kHzsignal 1 6,362 6,451signal 3 6,619 6,738signal 4 6,362 6,547

Finally it can be concluded that signal 3 with 140 kHz willgive the best results. Because of the excitation frequency of140 kHz, the received signals will have a big amplitude whichmake them easy to distinguish from noise. Signal 3 has thebiggest multiplication factor concerning the arrival of the directS0 wave.

VIII. DIFFERENT POLARISATION OF PIEZOELECTRICS

With the equipment used, it is not immediately possible to ap-ply delays. To make some steering of the area with constructiveinterference possible, the polarisation of the piezoelectrics waschanged by changing the connections. In figure 19, the propa-gation of the signal is predicted. As told before, when the fouractuators have the same polarisation, the signal has constructive

interference in front of the array. When A1 and A4 are actu-ated with an opposite polarisation, the areas with constructiveinterference are not well defined. This because the interspace istoo big and grating lobes are present. When A2 and A3 are ac-tuated with an opposite polarisation, the area with constructiveinterference is quite big. When the four actuators are actuatedand the last two have an opposite polarisation, the areas withconstructive interference are best defined. For this reason, theconnections of the A3 and A4 transducer were changed on theplate.

In figure 20, experimental results with signal 3 at a frequencyof 200 kHz are shown. When focusing on the S0 mode, itis known that this mode arrives in the sensors after a time of130, 6 µs and leaves 25 µs later. The signal in C2 is only a littlebit stronger when the polarisation of A3 and A4 is changed. Thisis because C2 is not exactly in the area of constructive interfer-ence as can be seen in figure 19. The constructive interferencein C2 can be noticed in the results obtained with a different po-larisation of A1 and A4 and with a different polarisation of A2and A3.

Fig. 15. Constructive interference of the array: (a) signals in C1, (b) signals inC2

IX. CONCLUSIONS

The program written was verified by experiments. Now, thebehavior of a phased array of PWAS transducers can be simu-lated. Steering of the signal was proved and a better dampingfunction was obtained for a particular frequency (200 kHz). Aninterface was made to see the influence of the different parame-ters faster.

The constructive interference with two actuators was shown.It was in good agreement with the programmed results. Be-cause no phasing of the signals was possible, the polarisation ofsome actuators was switched. The constructive interference waspredicted by the program written and later, it was seen that theamplitude of the S0 mode was stronger in the control sensor inthe area of the constructive interference.

REFERENCES

[1] Nondestructive Testing Resource Center, http://www.ndt-ed.org,[2] Victor Giurgiutiu and Jingjing Bao, Embedded-ultrasonics structural radar

for nondestructive evaluation of thin-wall structures, IMECE, 2002.[3] Victor Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer

Actie Sensors, 16th International Conference of Adaptive Structures andTechnologies ICAST-2005, 10-12 October 2005, Paris, France,

[4] National Instruments documentation, http://zone.ni.com,

Fig. 16. Signals studied: (a) signal 1, (b) signal 2, (c) signal 3, (d) signal 4

Fig. 17. Power spectrum of the different signals

Fig. 19. Influence of polarisation, visualisation of signal at 0,00014 s: (a) fouractuators with same polarisation, (b) A1 and A4 with different polarisation,(c) A2 and A3 with different polarisation, (d) A1 and A2 with differentpolarisation then A3 and A4

Fig. 20. Simulation results: signals in C1

Contents

Preface i

Summary ii

Resumo iii

Samenvatting iv

0.1 Inleiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

0.2 Beschrijving van het geschreven programma . . . . . . . . . . . . . . . . . v

0.2.1 Radiale propagatie . . . . . . . . . . . . . . . . . . . . . . . . . . . v

0.2.2 Eerste reflecties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

0.2.3 Toegepaste delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

0.2.4 Enkele resultaten . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

0.3 Experimentele setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

0.4 Invloed van de frequentie . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

0.4.1 Dempingfunctie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

0.4.2 Resonantiefrequentie . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

0.5 Resultaten met twee actuatoren . . . . . . . . . . . . . . . . . . . . . . . . xiv

0.6 Constructieve interferentie met een array van vier actuatoren . . . . . . . . xv

0.7 Verschillende toegepaste signalen . . . . . . . . . . . . . . . . . . . . . . . xv

0.8 Poging tot sturen van het signaal . . . . . . . . . . . . . . . . . . . . . . . xvii

Extended abstract xx

Contents xxviii

Acronyms xxxi

List of Figures xxxii

List of Tables xxxvi

xxviii

Contents

1 Introduction 1

1.1 Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Lamb waves and Piezoelectric Wafer Active Sensors . . . . . . . . . . . . . 2

1.3 Phased Array Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Ultrasonic inspection 5

2.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Near field distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Wave traveling through two different materials . . . . . . . . . . . . . . . . 9

2.5 Lamb waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Conventional ultrasonic transducers . . . . . . . . . . . . . . . . . . . . . . 12

2.6.1 PWAS transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 General principles of phased arrays 16

3.1 History of Phased Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Grating lobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Phased array transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 The applied delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5.1 1-D PWAS configuration . . . . . . . . . . . . . . . . . . . . . . . . 26

3.5.2 2-D PWAS configuration . . . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Imaging basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6.1 A-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6.2 B-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6.3 C-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6.4 S-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.6.5 Combined formats . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Phased arrays in Structural Health Monitoring 36

4.1 Phased array sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Embedded-Ultrasonic Radar algorithm . . . . . . . . . . . . . . . . . . . . 38

5 Simulation of phased array wave propagation 40

5.1 Program description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Hanning window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1.2 Radial propagation of the signal . . . . . . . . . . . . . . . . . . . . 42

5.1.3 Primary boundary reflections . . . . . . . . . . . . . . . . . . . . . 42

5.1.4 Phase delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

xxix

Contents

5.1.5 Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 S0 wave propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.1 One actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.2 Three actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2.3 Seven actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3 Total wave propagation, primary reflections included . . . . . . . . . . . . 47

6 Numerical simulations 50

6.1 Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.2 Simulated Z displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.3 Simulated Y displacements in 2 nodes above each other . . . . . . . . . . . 52

6.4 Simulated displacements in 4 adjacent nodes . . . . . . . . . . . . . . . . . 53

6.5 Simulated displacements in 8 adjacent nodes . . . . . . . . . . . . . . . . . 53

7 Experimental results 56

7.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.2 First series of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.2.1 Verification new equipment . . . . . . . . . . . . . . . . . . . . . . 59

7.2.2 Variation of frequency . . . . . . . . . . . . . . . . . . . . . . . . . 60

7.2.3 Damping function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.3 Second series of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.4 Third series of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.5 Fourth series of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7.5.1 Constructive interference with the array . . . . . . . . . . . . . . . 66

7.5.2 Influence of more actuators: internal impedance . . . . . . . . . . . 67

7.5.3 Different actuation signals . . . . . . . . . . . . . . . . . . . . . . . 68

7.6 Fifth series of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

8 Conclusions and further research 74

8.1 Obtained results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Bibliography 76

xxx

Acronyms

cg group velocity of Lamb waves

cLa Lamb wave velocity

cP pressure wave velocity

cS shear wave velocity

NDT Non-Destructive Testing

NI National Instruments

PCI Peripherical Component Interconnect

PWAS Piezoelectric Wafer Active Sensor

PXI PCI eXtensions for Instrumentation

RC Reflection Coefficient

SHM Structural Health Monitoring

Z Acoustic impedance of a medium

xxxi

List of Figures

1 Dispersief karakter van Lamb waves . . . . . . . . . . . . . . . . . . . . . . v

2 Radiale propagatie van het signaal: (a) zonder reflecties, (b) met reflecties vi

3 Uniforme lineare array van M actuators met tussenruimte d . . . . . . . . vii

4 Variatie van de tussenruimte met zeven actuatoren . . . . . . . . . . . . . viii

5 Variatie van de richting van constructieve interferentie . . . . . . . . . . . viii

6 De onderzochte platen: (a) Beschadigd, met netwerk van transductoren, (b)

Onbeschadigd, met array van vier transductoren en twee controletransduc-

toren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

7 Invloed van de frequentie op de verkregen signalen in sensor 1 met actuator 2 xi

8 Invloed van de frequentie op de verkregen signalen in sensor 3 met actuator 2 xi

9 Variatie van de amplitude van de S0 en A0 signalen met frequentie . . . . . xii

10 Finale vergelijking: (a) sensor 1 - actuator 2, (b) sensor 3 - actuator 2 . . . xiii

11 Power spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

12 Resulten met twee actuatoren, signaal in sensor 2: (a) experimentele resul-

taten, (b) geprogrammeerde resultaten . . . . . . . . . . . . . . . . . . . . xiv

13 Constructieve interferentie met een array : (a) signalen in C1, (b) signalen

in C2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

14 Bestudeerde signalen: (a) signaal 1, (b) signaal 2, (c) signaal 3, (d) signaal 4 xvi

15 Power spectrum van de verschillende signalen . . . . . . . . . . . . . . . . xvi

16 Ontvangen signalen met signaal 3: (a) 80 kHz in C1, (b) 80 kHz in C2, (c)

140 kHz in C1, (d) 140 kHz in C2, (e) 200 kHz in C1, (f) 200 kHz in C2 . . xviii

17 Invloed van de polarisatie: (a) vier actuatoren, zelfde polarisatie, (b) A1 en

A4, verschillende polarisatie, (c) A2 en A3, verschillende polarisatie, (d) A1

en A2 met tegengestelde polarisatie dan A3 en A4 . . . . . . . . . . . . . . xix

18 Experimentele resultaten: (a) signalen in C1, (b) signalen in C2 . . . . . . xix

2.1 Typical pulse-echo system . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

xxxii

List of Figures

2.2 Longitudinal and shear waves . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Sound field of a transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Snell’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Simulation of Lamb wave particle motion: (left) S0 symmetric mode; (right)

A0 anti-symmetric mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.6 Group velocity of the S0 and A0 mode vs. frequency . . . . . . . . . . . . . 12

2.7 Excitation sweet spot experimentally observed in an aluminum plate . . . . 15

3.1 Interference pattern of two sources . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Medical application of phased arrays . . . . . . . . . . . . . . . . . . . . . 17

3.3 Portable phased array equipment . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Different wave forms: (a) linear, (b) angled and (c) focused wave form . . . 21

3.5 Wave front of phased arrays: without grating lobes (left) and with grating

lobes (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Phased array probe: cross-section . . . . . . . . . . . . . . . . . . . . . . . 24

3.7 Different element patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.8 Wave fronts in near field (a) and far field (b) of a PWAS array . . . . . . . 26

3.9 Uniform linear array of M omni-directional sensors . . . . . . . . . . . . . 27

3.10 Coordinate system with O the center of the M PWAS . . . . . . . . . . . . 28

3.11 A-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.12 Single Value B-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.13 Cross sectional B-Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.14 C-Scan with a phased array transducer in progress . . . . . . . . . . . . . . 33

3.15 Phased Array Linear Sectoral Scan . . . . . . . . . . . . . . . . . . . . . . 34

3.16 Phased Array Angular Sectoral Scan . . . . . . . . . . . . . . . . . . . . . 35

3.17 Phased Array Angular Sectoral Scan . . . . . . . . . . . . . . . . . . . . . 35

4.1 Phased array on a plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Normalized ψ(ϑ) with a mass located at 100° (left) and 130° (right) . . . . 37

4.3 Uniform linear array of M omni-directional sensors (PWAS) spaced at pitch d 38

4.4 The basis of pulse-echo method: (a) transmitted smooth-windowed tone-

burst; (b) received signal to be analyzed . . . . . . . . . . . . . . . . . . . 39

5.1 Hanning window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 Radial propagation of signal with one actuator: (a) at time 0,0000625 s, (b)

along x = 750 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

xxxiii

List of Figures

5.4 Three sensors in a network configuration . . . . . . . . . . . . . . . . . . . 46

5.5 Signal propagation with seven actuators . . . . . . . . . . . . . . . . . . . 47

5.6 Variation of interspacing with seven actuators . . . . . . . . . . . . . . . . 48

5.7 Variation of steering angle with seven actuators . . . . . . . . . . . . . . . 48

5.8 Total wave propagation with reflections: (a) at time 1,045 ms, (b) compar-

ison between programmed and experimental obtained result . . . . . . . . 49

5.9 Seven actuators steered to 50° using S0 velocity, different interspacing: (a)

7.5 mm, (b) 15 mm, (c) 20 mm . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1 SHELL63 geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2 Simulated Z-displacement in actuator 1: (a) XY-plot, (b) Z-displacement in

sensor 2, (c) Z-displacement in sensor 3 . . . . . . . . . . . . . . . . . . . . 52

6.3 Simulated Z-displacement in actuator 1 . . . . . . . . . . . . . . . . . . . . 52

6.4 Simulated Y-displacement in 2 adjacent nodes . . . . . . . . . . . . . . . . 53

6.5 Simulated displacements in 4 adjacent nodes to the actuator: signals ob-

tained in 4 points at an equal distance . . . . . . . . . . . . . . . . . . . . 54

6.6 Simulated displacements in 8 adjacent nodes to the actuator: (a) simulated

displacements, (b) signals obtained in 4 points at an equal distance . . . . 54

6.7 Results from numerical simulations and experimental results, actuator 2 . . 55

7.1 The equipment and plate in the laboratorium . . . . . . . . . . . . . . . . 57

7.2 Plates under investigation: (a) Damaged plate with network of transducers,

(b) Non-damaged plate with array of transducers and two control transducers 58

7.3 Some details of the setup: (a) array on plate, (b) cable connections . . . . 58

7.4 Comparison between results obtained with actuator 1 and sensor 2: (a) old

equipment, (b) new equipment . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.5 Influence on frequency on obtained signal in sensor 1 with actuator 2 . . . 61

7.6 Influence on frequency on obtained signal in sensor 3 with actuator 2 . . . 62

7.7 Variation of the amplitude of the S0 and A0 wave package with frequency,

actuator 2 actuated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

7.8 Final comparison with adapted damping function: (a) sensor 1 - actuator

2, (b) sensor 3 - actuator 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7.9 Power spectrum of the signal in sensor C1 . . . . . . . . . . . . . . . . . . 65

7.10 Results with two actuators, signals taken in sensor 2: (a) experimental re-

sults, (b) programmed results . . . . . . . . . . . . . . . . . . . . . . . . . 66

7.11 Programmed propagation of the signal: (a) 0,00007 s, (b) 0,0001 s . . . . . 67

xxxiv

List of Figures

7.12 Constructive interference of the array: (a) signals in C1, (b) signals in C2 . 67

7.13 Influence of more actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

7.14 Signals studied: (a) signal 1, (b) signal 2, (c) signal 3, (d) signal 4 . . . . . 69

7.15 Power spectrum of the different signals . . . . . . . . . . . . . . . . . . . . 70

7.16 Received signals with signal 3: (a) 80 kHz in C1, (b) 80 kHz in C2, (c) 140

kHz in C1, (d) 140 kHz in C2, (e) 200 kHz in C1, (f) 200 kHz in C2 . . . . 71

7.17 Received signals in C1: (a) signal 1, 140 kHz, (b) signal 1, 200 kHz, (c)

signal 3, 140 kHz, (d) signal 3, 200 kHz, (e) signal 4, 140 kHz, (f) signal 4,

200 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.18 Influence of polarisation, visualisation of signal at 0,00014 s: (a) four ac-

tuators with same polarisation, (b) A1 and A4 with different polarisation,

(c) A2 and A3 with different polarisation, (d) A1 and A2 with different

polarisation then A3 and A4 . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.19 Experimental results: (a) signals in C1, (b) signals in C2 . . . . . . . . . . 73

xxxv

List of Tables

1 Coordinaten van de transducers . . . . . . . . . . . . . . . . . . . . . . . . ix

2 Afgelegde afstand van de signalen van actuator i tot sensor j . . . . . . . . x

3 Amplitude van het signaal in functie van de afstand tot de actuator . . . . xii

4 Resonantiefrequentie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

5 Vermenigvuldigingsfactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

6.1 Parameter specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1 Coordinates of the transducers . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.2 Traveling distance of wave packages from one actuator to one sensor . . . . 60

7.3 Arrival time of wave packages in sensor 1 . . . . . . . . . . . . . . . . . . . 61

7.4 Arrival time of wave packages in sensor 3 . . . . . . . . . . . . . . . . . . . 61

7.5 Wave amplitude in function of distance from the actuator . . . . . . . . . . 63

7.6 Natural frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.7 Multiplication factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

xxxvi

Chapter 1

Introduction

1.1 Structural Health Monitoring

Structural Health Monitoring (SHM) is an emerging technology leading to the development

of integrated systems capable of continuously monitoring structures. SHM refers to the

broad concept of assessing the ongoing, in-service performance of structures using a variety

of measurement techniques. The related technologies created an exciting new field within

various branches of engineering. The ultimate goal of SHM is to increase reliability, improve

safety, enable light-weight design and reduce maintenance costs for all kinds of structures.

SHM involves integration of Nondestructive Testing(NDT) methods into a system in order

to improve damage detection and minimize the human intervention. NDT allows parts

and materials to be inspected and measured without damaging them. The field of Non-

destructive Tests (NDT) is a very broad, interdisciplinary field that plays a critical role

in assuring that structural components and systems perform their function in a reliable

and cost effective fashion. NDT technicians and engineers define and implement tests that

locate and characterize material conditions and flaws that might otherwise cause planes to

crash, reactors to fail, trains to derail, and a variety of less visible, but equally troubling

events. Actual NDT systems in aircrafts are stationary and ground based which imply

that the aircraft is on the ground whenever it needs to be inspected. Aircrafts have regular

mandatory inspections and every minute that an aircraft is on the ground is an extra cost

to the company due to the non-operation. With the new SHM systems, the mandatory

periodic procedures will be reduced which will result in a reduction in the maintenance

costs.

1

Chapter 1. Introduction

In the early 1970’s, NDT investigators found out that a part with a crack does not need

to be rejected immediately. It became possible to accept structures containing defects if

the sizes of those defects were known. This formed the basis for a new design philosophy

called ”‘damage tolerant design”’. Components that have known defects could continue to

be used as long as it could be established that those defects would not grow to a critical

size that would result in catastrophic failure. Now, also quantitative information about

flaw size was necessary to allow fracture mechanic calculations to predict the remaining life

of a component. These needs led to the creation of a number of research programs around

the world and the emergence of nondestructive evaluation (NDE) as a new discipline. NDE

is used to describe measurements that are more quantitative in nature.

1.2 Lamb waves and Piezoelectric Wafer Active Sen-

sors

Ultrasonic testing is one of the NDT methods. Current ultrasonic inspection of thin wall

structures (e.g., aircraft shells, storage tanks, large pipes, etc.) is a time consuming opera-

tion that requires meticulous through-the-thickness C-scans over large areas. One method

to increase the efficiency of thin-wall structures inspection is to use guided waves (e.g.,

Lamb waves) instead of the conventional pressure waves. Guided waves propagate along

the mid-surface of thin-wall plates and shallow shells. They can travel at relatively large

distances with very little amplitude loss and offer the advantage of large-area coverage with

a minimum of installed sensors. Guided Lamb waves have opened new opportunities for

cost-effective detection of damage in aircraft structures.

Traditionally, guided waves have been generated by impinging the plate obliquely with

a tone-burst from a relatively large ultrasonic transducer that generates simultaneously

pressure and shear waves into the thin plate. However, conventional Lamb-wave probes

(wedge and comb transducers) are relatively too heavy and expensive to be considered for

widespread deployment on an aircraft structure as a part of a SHM system. In recent years,

several investigators have explored the generation of Lamb-waves with piezoelectric wafer

active sensors (PWAS). PWAS are inexpensive, non-intrusive, un-obtrusive and minimally

invasive devices that can be surface-mounted on existing structures or inserted between

the layers of lap joints or inside composite materials. PWAS couple their in-plane motion,

excited by the applied oscillatory voltage through the piezoelectric effect, with the Lamb-

waves particle motion on the material surface.

2

Chapter 1. Introduction

1.3 Phased Array Actuators

Ultrasonic phased array transducers have been around for more then three decades. They

were initially used in medical applications. They are also used in acoustics and antenna

theory in order to actively shift the direction that an array listens or transmits. For an array

which is mobile, the array can be physically steered to look in specific directions. Arrays

which can not be physically steered can still be pointed to listen or transmit in specific

directions using the appropriate signal processing. The combination of phased arrays

along with wave mechanics models can be used in a damage detection scheme to actively

interrogate a structure to search for discontinuities. This can be done by simple pulse-

echo scanning approach where the array sends out a plane wave in a particular direction

and senses in the same direction for any reflections. The presence of a reflection would

then indicate a discontinuity and the position of the discontinuity can be determined.

The work outlined in this paper investigates the steering possibilities of phased arrays.

Some simulations were performed and later this simulation results were compared with

experimental obtained data.

1.4 Thesis Outline

Chapter 2 gives a description of the ultrasonic inspection technique. Some topics that

will be important for the later work are noticed and Lamb waves are introduced. The

transducers used for ultrasonic inspection are described.

In chapter 3 the basic principles of phased arrays are given. This chapter starts with a

historic overview. Later, the possibilities with phased arrays are shown. The phenomenon

of grating lobes is explained and the calculation of the applied delays is defined. This

chapter ends with a description of the possibilities to make the results visible.

Chapter 4 describes the results from other investigators. Purekar and Pines used a

phased array to receive signals. Giurgiutiu stated the Embedded-Ultrasonic Structural

Radar (EUSR) algorithm.

Chapter 5 consists of two parts. The first part explains the program written to simulate

the Lamb wave propagation. The second part gives some results. This chapter shows also

the Guided User Interface (GUI) that was made.

3

Chapter 1. Introduction

In chapter 6, it was tried to make a numerical simulation of the Lamb wave propagation.

As the version of ANSYS that was used for this project, was not able to simulate piezo-

electric behavior, neither could simulate a radial signal, much obstacles were encountered.

The experiments done are described in chapter 7. This chapter start with a description of

the experimental setup. It goes on with a study of the frequency of the applied signal. The

natural frequency for the system under investigation is found. After this, the damping

function from the program is optimised to agree better with the results. An optimal

actuation signal is also found. Furthermore, the influence of more actuators is studied.

The interference from two actuators at a distance away from each other is proved by

considering the signal in a sensor a distance away from both actuators. Finally, an array

of four actuators was studied and the constructive interference was made visible by using

two sensors.

4

Chapter 2

Ultrasonic inspection

Damage detection for beams and plates is an area of active research since many components

of aerospace systems can be modeled as beams or plates. One approach which can be taken

for damage detection relies on a modal analysis approach to the structural dynamics.

Sensors placed on different locations can determine the modes and natural frequencies of

the structure. Damage in a structure would result in shifts in natural frequencies of the

structure and changes in the modes. However, the natural frequencies and modes do not

shift significantly due to small incipient damage cases. In order to get better resolution,

the order of the system is increased by adding more elements which can result in a high

computation cost. Another method of damage detection is to use ultrasonic techniques to

examine specific locations on the structure. This method is powerful in that small damage

cases can be detected. However, the ultrasonic techniques need to be local to the damage

and much time and effort would go into scanning the entire structure. This chapter will

give a basic introduction to ultrasonic testing.

2.1 General description

Ultrasonic test instruments have been used in industrial applications for more than sixty

years. Since the 1940s, the laws of physics that govern the propagation of high frequency

sound waves through solid materials have been used to detect hidden cracks, voids, poros-

ity, and other internal discontinuities in metals, composites, plastics, and ceramics, as well

as to measure thickness and analyze material properties. Ultrasonic testing is completely

nondestructive and safe, and it is a well established test method in many basic manu-

facturing processes, and service industries, especially in applications involving welds and

5

Chapter 2. Ultrasonic inspection

structural metals.

Ultrasonic testing is done by transmission of high-frequency sound waves into a material.

The aim of this is to detect imperfections or to locate changes in material properties. Two

basic techniques are being generally used: pitch-catch and pulse-echo. The pitch-catch

method used two transducers, one to transmit, the other to receive the signal. The pulse-

echo method used one transducer to send a short signal (pulse) and to detect the echoes

of this signal generated by the backscatter of the signal from various material defects.

To illustrate this last inspection principle, a typical pulse-echo inspection configuration is

illustrated in figure 2.1.

Figure 2.1: Typical pulse-echo system

In ultrasonic testing, the inspector must make a decision about the frequency of the trans-

ducer that will be used. The speed of sound c is constant and equal to λ · f with λ the

wavelength and f the frequency of the sound wave. By increasing the frequency, the wave-

length of the sound will decrease. The wavelength of the ultrasound used has a significant

effect on the probability of detecting a discontinuity. A general rule of thumb is that a

discontinuity must be larger than one-half the wavelength to stand a reasonable chance of

being detected. One also needs to take account that when sound travels through a medium,

its intensity diminishes with distance. [2]

In solids, sound waves can propagate in four principle modes that are based on the way the

6

Chapter 2. Ultrasonic inspection

particles oscillate. Sound can propagate as longitudinal waves, shear waves, surface waves,

and in thin materials as plate waves. Longitudinal and shear waves are the two modes

of propagation most widely used in ultrasonic testing. The particle movement responsible

for the propagation of longitudinal and shear waves is illustrated in figure 2.2. Waves that

move in the same direction, or are parallel to their source are called longitudinal waves.

Longitudinal sound waves are the easiest to produce and have the highest speed, however,

it is possible to produce other types. Waves which move perpendicular to the direction the

wave propagates are called shear waves or transverse waves. Shear waves travel at slower

speeds than longitudinal waves, and can only be made in solids. Think of a stretched out

slinky, you can create a longitudinal wave by quickly pushing and pulling one end of the

slinky. This causes longitudinal waves for form and propagate to the other end. A shear

wave can be created by taking the end and moving it up and down, this causes the slinky

to create a wave (which looks more like the oceans waves you see) to move down to the

other end. Another type of wave is the surface wave. Surface waves travel at the surface

of a material and particles move in elliptical orbits. They are slightly slower than shear

waves but difficult to make. A final type of sound wave is the plate wave. These waves

also move in elliptical orbits but are much more complex. They can only be created in

very thin pieces of material.

Figure 2.2: Longitudinal and shear waves

7

Chapter 2. Ultrasonic inspection

2.2 Near field distance

The sound field of a transducer is divided into two zones, the near field and the far field.

The near field is the region close to the transducer where the sound pressure goes through

a series of maximums and minimums, and it ends at the last on-axis maximum at a

certain distance from the face. The near field distance represents the natural focus of

the transducer and represents the greatest distance at which a transducer’s beam can be

focused by means of either an acoustic lens or phasing techniques. The far field is the

region beyond this distance where the sound pressure gradually drops to zero as the beam

diameter expands and its energy dissipates.

Figure 2.3: Sound field of a transducer

2.3 Attenuation

As it travels through a medium, the organized wave front generated by an ultrasonic

transducer will begin to break down due to imperfect transmission of energy through the

micro structure of any material. Organized mechanical vibrations (sound waves) turn

into random mechanical vibrations (heat) until the wave front is no longer detectable.

This process is known as sound attenuation. The mathematical theory of attenuation

8

Chapter 2. Ultrasonic inspection

and scattering is complex. The loss of amplitude due to attenuation across a given sound

path will be the sum of absorption effects, which increase linearly with frequency, and

scattering effects, which vary through three zones depending on the ratio of the size of

grain boundaries or other scatterers to wavelength. In all cases, scattering effects increase

with frequency so higher frequencies will be attenuated more rapidly than lower frequencies

in any medium. For this reason, low test frequencies are usually employed in materials

with high attenuation coefficients like low density plastics and rubber.

2.4 Wave traveling through two different materials

When a sound wave traveling through a medium encounters a boundary with a dissimilar

medium that lies perpendicular to the direction of the wave, a portion of the wave energy

will be reflected straight back and a portion will continue straight ahead. The percentage

of reflection versus transmission is related to the relative acoustic impedances of the two

materials, with acoustic impedance in turn being defined as material density multiplied by

speed of sound. The reflection coefficient (RC) at a planar boundary, the percentage of

sound energy that is reflected back to the source, may be calculated as follows:

RC =Z2 − Z1

Z2 + Z1

(2.1)

with Z1 the acoustic impedance of the first medium and Z2 the acoustic impedance of the

second medium. From this equation it can be seen that as the acoustic impedances of the

two materials become more similar, the reflection coefficient decreases, and as the acoustic

impedances become less similar, the reflection coefficient increases. In theory the reflection

from the boundary between two materials of the same acoustic impedance is zero, while in

the case of materials with very dissimilar acoustic impedances, as in a boundary between

steel and air, the reflection coefficient approaches 100%.

When a sound wave traveling through a material encounters a boundary with a different

material at an angle other than zero degrees, a portion of the wave energy will be reflected

forward at an angle equal to the angle of incidence. At the same time, the portion of the

wave energy that is transmitted into the second material will be refracted in accordance

with Snell’s Law. Snell’s law related the sines of the incident and refracted angle to the

wave velocity in each material as diagrammed below.

9

Chapter 2. Ultrasonic inspection

Figure 2.4: Snell’s law

If sound velocity in the second medium is higher than that in the first, then above certain

angles this bending will be accompanied by mode conversion, most commonly from a

longitudinal wave mode to a shear wave mode. This is the basis of widely used angle

beam inspection techniques. As the incident angle in the first (slower) medium such as a

wedge or water increases, the angle of the refracted longitudinal wave in the second (faster)

material such as metal will increase. As the refracted longitudinal wave angle approaches

90 degrees, a progressively greater portion of the wave energy will be converted to a lower

velocity shear wave that will be refracted at the angle predicted by Snell’s Law. At incident

angles higher than that which would create a 90 degree refracted longitudinal wave, the

refracted wave exists entirely in shear mode. A still higher incident angle will result in a

situation where the shear wave is theoretically refracted at 90 degrees, at which point a

surface wave is generated in the second material.

2.5 Lamb waves

Current ultrasonic inspection of thin wall structures is a time consuming operation that

requires meticulous through-the-thickness C-scans over large areas. One method to increase

the efficiency of thin-wall structures inspection is to utilize guided waves (e.g., Lamb waves)

instead of the conventional pressure waves. Guided waves propagate along the mid-surface

of thin-wall plates and shallow shells. They can travel at relatively large distances with

very little amplitude loss and offer the advantage of large-area coverage with a minimum

of installed sensors. Guided Lamb waves have opened new opportunities for cost-effective

detection of damage in aircraft structures. Snell’s law ensures mode conversion at the

interface, hence a combination of pressure and shear waves are simultaneously generated

into the thin plate. [7]

10

Chapter 2. Ultrasonic inspection

Wave speed is one of the most important parameters for ultrasonic testing. The Lamb

wave speed is obtained by solving the Rayleigh-Lamb equation. First, define ξ =√c2S/c

2P ,

ς =√c2S/c

2La and d = kSd, where cLa is the Lamb wave speed and d is the half thickness of

the plate. The shear wave velocity cS and pressure wave velocity cP are defined as follows:

cS =

√E

2ρ(1 + ν)and cP =

√νE

(1 + ν)(1− 2ν)ρ+

E

ρ(1 + ν)(2.2)

with ρ is the mass density, E the elasticity modulus and ν the shear modulus of the material.

In addition, also define Lamb wave number kL = ωcLa

, kP = ωcP

, kS = ωcS

and the variables

q =√k2L − k2

P , s =√k2L − k2

S. [8]

For symmetrical motion (Figure 2.5), the Rayleigh-Lamb frequency equation can be written

astan(√

1− ς2dtan(

√ξ2 − ς2)

+4ς2√

1− ς2√ξ2 − ς2

(2ς2 − 1)2= 0 (2.3)

Then one can write the two components of the displacement as

U(x, z, t) = Re[AkL(cosh(qz)

sinh(qd)− 2qs

k2L + s2

cosh(sz)

sinh(sd))ei(kLx−ωt

π2) (2.4)

W (x, z, t) = Re[Aq(sinh(qz)

sinh(qd)− 2k2

L

k2L + s2

sinh(sz)

sinh(sd))ei(kLx−ωt) (2.5)

For anti-symmetric motion (Figure 2.5), the Rayleigh-Lamb frequency equation is

tan(√

1− ς2dtan(

√ξ2 − ς2)

+(2ς2 − 1)2

4ς2√

1− ς2√ξ2 − ς2

= 0 (2.6)

The two components of the anti-symmetric displacement can be expressed as

U(x, z, t) = Re[AkL(cosh(qz)

cosh(qd)− 2qs

k2L + s2

cosh(sz)

cosh(sd))ei(kLx−ωt

π2) (2.7)

W (x, z, t) = Re[Aq(sinh(qz)

cosh(qd)− 2k2

L

k2L + s2

sinh(sz)

cosh(sd))ei(kLx−ωt) (2.8)

11

Chapter 2. Ultrasonic inspection

Figure 2.5: Simulation of Lamb wave particle motion: (left) S0 symmetric mode; (right) A0

anti-symmetric mode

The group velocity of Lamb waves is important when examining the traveling of Lamb

wave packs as will be done later in this work. To calculate the group velocity of Lamb

waves, the following formula is used:

cg = c2La[cLa − (fd)dcLad(fd)

]−1 (2.9)

where c is the Lamb wave phase velocity. Figure 2.6 shows a plot of the group velocities

vs. frequency.

Figure 2.6: Group velocity of the S0 and A0 mode vs. frequency

2.6 Conventional ultrasonic transducers

Conventional monolithic ultrasonic transducers for NDT applications come in a wide vari-

ety of sizes, frequencies, and case styles, but most have a common internal structure. Typ-

ically, the active element of the transducer is a thin disk, square, or rectangle piezoelectric

12

Chapter 2. Ultrasonic inspection

ceramic that converts electrical energy into mechanical energy (ultrasonic vibrations), and

vice versa. It is protected from damage by a wear plate or acoustic lens, and backed by

a block of damping material that quiets the transducer after the sound pulse has been

generated. This ultrasonic subassembly is mounted in a case with appropriate electrical

connections.

As voltage is applied, the piezoelectric transducer element (often called a crystal) deforms

by compressing in the direction perpendicular to its face. When the voltage is removed,

typically less than a microsecond later, the element springs back, generating the pulse

of mechanical energy that comprises an ultrasonic wave. To generate obliquely incident

waves, a wedge-transducer is needed. Due to the complexity of their construction, tra-

ditional ultrasonic transducers are bulky. The advent of commercially available low-cost

piezoceramics wafers has opened new opportunities for ultrasonic testing. Through their

intrinsic electro-mechanical coupling, the piezoceramics can act as both sensors and actu-

ators.

2.6.1 PWAS transducers

Giurgiutiu and Bao studied the properties of piezoelectric-wafer active sensors (PWAS).

[7] PWAS are inexpensive, non-intrusive, un-obtrusive and minimally invasive devices that

can be surface-mounted on existing structures inserted between the layers of lap joints, or

inside composite materials. PWAS operated on the piezoelectric principle that couples the

electrical and mechanical variables in the material:

Sij = sijklTkl + dkijEk (2.10)

Dj = djklTkl + εjkEk (2.11)

with Sij the mechanical strain, Tkl the mechanical stress, Ek the electric field, Dj the

electrical displacement, sijkl the mechanical compliance of the material measured at zero

electric field (E = 0), dkij the piezoelectric coupling coefficient and εjk the dielectric per-

mittivity measured at zero mechanical stress (T = 0). For embedded NDE applications,

PWAS couple their in-plane motion, excited by the applied oscillatory voltage through the

piezoelectric effect, with the Lamb waves-particle motion on the material surface. PWAS

probes can act as both exciters and sensors of the elastic Lamb waves traveling in the

material. In this work, PWAS will be used for far-field damage detection using pulse-echo

and pitch-catch methods.

13

Chapter 2. Ultrasonic inspection

The main advantage of PWAS over conventional ultrasonic probes lies in their small size,

lightweight, low profile and small cost. PWAS operation is different from that of conven-

tional ultrasonic probes in the following aspects:

� PWAS achieve Lamb wave excitation and sensing through surface ”‘pinching”’ (in

plane strains), while conventional ultrasonic probes excite through surface ”‘tapping”’

(normal stress).

� PWAS are strongly coupled with the structure and follow the structural dynamics,

while conventional ultrasonic probes are relatively free from the structure and follow

their own dynamics.

� PWAS are non-resonant wide-band devices, while conventional ultrasonic probes are

narrow-banded resonators.

The excitation of Lamb waves in plates with PWAS transducers is studied by considering

the excitation applied by the PWAS through a surface stress τ = τa(x)eiωt. Applying a

space-domain Fourier transform analysis of the basic Lamb wave equations yields the strain

wave and displacement wave solutions in the form:

εx(x, t) =1

2π

−i2µ

∫ −∞

∞(τNS

DS

+τNA

DA

)ei(εx−ωt)dε (2.12)

ux(x, t) =1

2π

−i2µ

∫ −∞

∞

1

ξ(τNS

DS

+τNA

DA

)ei(εx−ωt)dε (2.13)

where τ is the Fourier transform of τa(x), p2 = ω2

c2P−ξ2, q2 = ω2

c2S−ξ2, while c2P = (α+2µ)/ρ

and c2S = µ/ρ are the pressure (longitudinal) and shear (transverse) wave speeds, α and µ

are Lame constants, ρ is the mass density and

NS = ξq(ξ2 + q2) cos(ph) cos(qh) (2.14)

DS = (ξ2 − q2)2 cos(ph) sin(qh) + 4ξ2pq sin(ph) cos(qh) (2.15)

NA = ξq(ξ2 + q2) sin(ph) sin(qh) (2.16)

DA = (ξ2 − q2)2 sin(ph) cos(qh) + 4ξ2pq cos(ph) sin(qh) (2.17)

The integral in 2.12 and 2.13 is singular at the roots of DS and DA. The equations

DS = 0 and DA = 0 are exactly the Rayleigh-Lamb characteristic equations for symmetric

14

Chapter 2. Ultrasonic inspection

and anti-symmetric motions accepting the simple roots: ξ0S, ξ

1S, ξ

2S, ... ξ

0A, ξ

1A, ξ

2A, ... corre-

sponding to the symmetric (S) and anti-symmetric (A) Lamb waveguide modes. For ideal

bonding between the PWAS and the plate, the shear stress in the bonding layer and the

corresponding space-domain Fourier transform are:

τ(x) = aτ0[δ(x− a)− δ(x+ a)] , τa = aτ0[−2i sin ξa] (2.18)

with a half the length of the PWAS. Hence, the strain-wave solution becomes:

εx(x, t) = −iaτ0µ

∑ξS

sin(ξSa)NS(ξS)

D′S(ξS)

ei(ξSx−ωt) − iaτ0

µ

∑ξA

sin(ξAa)NA(ξA)

D′A(ξA)

ei(ξAx−ωt) (2.19)

Similarly, the displacement wave solution is obtained as:

ux(x, t) = −iaτ0µ

∑ξS

sin(ξSa)

ξSNS(ξS)

D′S(ξS)

ei(ξSx−ωt)−iaτ0

µ

∑ξA

sin(ξAa)

ξANA(ξA)

D′A(ξA)

ei(ξAx−ωt) (2.20)

Giurgiutiu [7] also noticed the remarkable fact that, at 300 kHz, the amplitude of the

A0 mode goes through zero, while that of the S0 is close to its peak. This represents an

excitation ”‘sweet spot”’ for S0 Lamb waves. This proves that frequencies can be found

for which the response is dominated by certain preferentially excited modes. This is called

wavelength-based tuning and can be seen in figure 2.7.

Figure 2.7: Excitation sweet spot experimentally observed in an aluminum plate

15

Chapter 3

General principles of phased arrays

3.1 History of Phased Arrays

The English scientist Thomas Young demonstrated in 1801 for the first time the principle

of constructive and destructive interaction of waves in an experiment utilising two point

sources of light to create interference patterns. Waves that combine in phase reinforce each

other, while waves that combine out-of-phase will cancel each other.

Figure 3.1: Interference pattern of two sources

The energy of the wave front emerging from two or more sources can be bended, steered,

16

Chapter 3. General principles of phased arrays

or focused by means of phase shifting, or phasing. Phasing means that the sources are

sequentially pulsed. In the 1960s, researchers began developing ultrasonic phased array

systems that utilized multiple point source transducers that were pulsed so as to direct

sound beams by means of these controlled interference patterns. In the early 1970s, com-

mercial phased array systems for medical diagnostic use first appeared, using steered beams

to create cross-sectional images of the human body.

Figure 3.2: Medical application of phased arrays

Initially, the use of ultrasonic phased array systems was largely confined to the medical

field, aided by the fact that the predictable composition and structure of the human body

make instrument design and image interpretation relatively straightforward. Industrial

applications, on the other hand, represent a much greater challenge because of the widely

varying acoustic properties of metals, composites, ceramics, plastics, and fiberglass, as well

as the enormous variety of thicknesses and geometries encountered across the scope of

industrial testing. The first industrial phased array system, introduced in the 1980s, were

extremely large, and required data transfer to a computer in order to do the processing

and image presentation. These systems were most typically used for in-service power

generation inspections. In large part, this technology was pushed heavily in the nuclear

17

Chapter 3. General principles of phased arrays

market, where critical assessment more greatly allows use of cutting edge technology for

improving probability of detection. Other early applications involved large forged shafts

and low pressure turbine components.

In the 1990s, portable, battery-powered phased array instruments for industrial use ap-

peared. Analog designs had required power and space to create the multi-channel configu-

rations necessary for beam steering, but the transition into the digital world and the rapid

development of inexpensive embedded microprocessors enabled more rapid development

of the next generation phased array equipment. In addition, the availability of low power

electronic components, better power-saving architectures, and industry-wide use surface

mount board design led to miniaturization of this advanced technology. This resulted in

phased array tools which allowed electronic setup, data processing, display and analysis all

within a portable device, and so the doors were opened to more widespread use across the

industrial sector. This in turn drove the ability to specify standard phased array probes

for common applications.

Nowadays, phased array systems are available in a variety of models with increasing com-

plexity and capability. Instruments range from basic models that perform simple sector and

linear scans with 16-element probes to advanced systems that offer multi-channel capability

and advanced interpretive software with probes of up to 256 elements.

Figure 3.3: Portable phased array equipment

18

Chapter 3. General principles of phased arrays

3.2 General description

An array is an organized arrangement of large quantities of an object (typically from 16 to

256). The simplest form of an ultrasonic array for NDT would be a series of several single

element transducers arranged in such a way as to increase inspection coverage and/or the

speed of a particular inspection. The different elements can be pulsed separately in a pro-

grammed pattern. This is called phasing. Inspections with ultrasonic arrays require high

speed multi-channel ultrasonic equipment with proper pulsers, receivers, and gate logic

to process each channel as well as careful fixturing of each transducer to properly set up

the inspection zones. While the elements in reality are much smaller than conventional

transducers, these elements can be pulsed as a group so as to generate directionally con-

trollable wavefronts. This ”Electronic Beam Forming” allows multiple inspection zones to

be programmed and analyzed at very high rates of speed from a single position transducer.

The four most important array parameters that have a number of interrelated effects on

performance are frequency, element size, number of elements and pitch and aperture.

� As noted before, the test frequency has a significant effect on near field length and

beam spreading. In practice, higher frequencies can provide better signal to noise

ratio than lower frequencies since they offer potentially sharper focusing and thus

a tighter, more optimized focal spot. At the same time, penetration in any test

material will decrease with frequency because of increasing material attenuation as

frequency goes up. Applications involving very long sound paths or test materials

that are highly attenuating or scattering will require use of lower frequencies. Com-

monly, industrial phased array probes are offered with frequencies between 1 MHz

and 15 MHz.

� As the size of individual elements in an array decreases, its beam steering capability

increases. The minimum practical element size in commercial probes is typically

around 0.2 mm. However if the element size is less than one wavelength, strong

unwanted side lobes will occur.

� As the number of elements in an array increases, so does the physical coverage area

of the probe and its sensitivity, focusing capability, and steering capability. At the

same time, use of large arrays must often need to be balanced against issues of system

complexity and cost.

19

Chapter 3. General principles of phased arrays

� Pitch is the distance between individual elements, aperture is the effective size of

a pulsing element that is usually comprised of a group of individual elements that

are pulsed simultaneously (virtual aperture). To optimize steering range, pitch must

be small. For optimum sensitivity, minimum unwanted beam spreading, and strong

focusing, the aperture must be large. Today’s phased array instruments most com-

monly support focal laws for up to 16 element apertures. More advanced systems

allow up to 32 or even 64 element apertures.

In phased array testing, the predictable reinforcement and cancellation effects caused by

phasing are used to shape and steer the ultrasonic beam. Pulsing individual elements or

groups of elements with different delays creates a series of point source waves that will

combine into a single wave front that will travel at a selected angle. By changing the

pattern of the delays, more steering possibilities occur. Through constructive interference,

the amplitude of this combined wave can be considerably greater than the amplitude of

any one of the individual waves that produce it. Similarly, variable delays are applied

to the echoes received by each element of the array to sum the responses in such a way

as to represent a single angular and/or focal component of the total beam. In addition

to altering the direction of the primary wave front, this combination of individual beam

components allows beam focusing at any point in the near field. Elements are usually

pulsed in groups of 4 to 32 in order to improve effective sensitivity by increasing aperture,

which reduces unwanted beam spreading and enables sharper focusing.

20

Chapter 3. General principles of phased arrays

Figure 3.4: Different wave forms: (a) linear, (b) angled and (c) focused wave form

Phased array systems pulse and receive from multiple elements of an array. Similarly, the

receiver function combines the input from multiple elements into a single presentation.

Because phasing technology permits electronic beam shaping and steering, it is possible to

generate a vast number of different ultrasonic beam profiles from a single probe assembly,

and this beam steering can be dynamically programmed to create electronic scans.

The benefits of phased array technology over conventional UT come from its ability to use

multiple elements to steer, focus and scan beams with a single transducer assembly. Beam

steering, commonly referred to sectoral scanning, can be used for mapping components at

appropriate angles. This can greatly simplify the inspection of components with complex

geometry. The small footprint of the transducer and the ability to sweep the beam without

21

Chapter 3. General principles of phased arrays

moving the probe also aids inspection of such components in situations where there is

limited access for mechanical scanning. Sectoral scanning is also typically used for weld

inspection. The ability to test welds with multiple angles from a single probe greatly

increases the probability of detection of anomalies. Electronic focusing permits optimizing

the beam shape and size at the expected defect location, as well as further optimizing

probability of detection. The ability to focus at multiple depths also improves the ability for

sizing critical defects for volumetric inspections. Focusing can significantly improve signal-

to-noise ratio in challenging applications, and electronic scanning across many groups of

elements allows for C-Scan images to be produced very rapidly.

The potential disadvantages of phased array systems are a somewhat higher cost and a

requirement for operator training, however these costs are frequently offset by their greater

flexibility and a reduction in the time required to perform a given inspection.

3.3 Grating lobes

A phenomenon associated with phased array probes is the generation of unwanted grating

lobes or side lobes, two closely related phenomena caused by sound energy that spreads

out from the transducer at angles other than the primary path. This phenomenon is not

limited to phased array systems: unwanted lobes also occur with conventional transducers

as element size increases. These unwanted ray paths can reflect off surfaces in the test piece

and cause spurious indications on an image. The amplitude of grating lobes is significantly

affected by pitch size, the number of elements, frequency, and bandwidth. The beam

profiles below compare two situations where the probe aperture is approximately the same,

but the beam at left is generated by six elements at 0.4 mm pitch and the beam at right

by three elements at 1 mm pitch. The beam at left is approximately shaped as a cone,

while the beam at right has two spurious lobes at approximately a 30 degree angle to the

center axis of the beam.

Grating lobes will occur whenever the size of individual elements in an array is equal to

or greater than the wavelength, and there will be no grating lobes when element size is

smaller than half a wavelength. For element sizes between one-half and one wavelength,

the generation of grating lobes will depend on the steering angle. Thus the simplest way

to minimize grating lobes in a given application is to use a transducer with a small pitch.

22

Chapter 3. General principles of phased arrays

Figure 3.5: Wave front of phased arrays: without grating lobes (left) and with grating lobes(right)

3.4 Phased array transducers

While phased array transducers come in a wide range of sizes, shapes, frequencies, and

number of elements, what they all have in common is a piezoelectric element that has been

divided into a number of segments. Contemporary phased array transducers for industrial

NDT applications are typically constructed around piezocomposite materials, which are

made up of many tiny, thin rods of piezoelectric ceramic embedded in a polymer matrix.

While they can be more challenging to manufacture, composite transducers typically offer

a 10 to 30 dB sensitivity advantage over piezoceramic transducers of otherwise similar

design. Segmented metal plating is used to divide the composite strip into a number of

electrically separated elements that can be pulsed individually. This segmented element is

then incorporated into a transducer assembly that includes a protective matching layer, a

backing, cable connections, and an overall housing. The transducer forms the mean part

of a phased array system and can by used with various types of wedges, in a contact mode,

or in immersion testing. His shape may be square, rectangular or round. Test frequencies

23

Chapter 3. General principles of phased arrays

are in the range from 1 to 10MHz.

Figure 3.6: Phased array probe: cross-section

Figure 3.6 depicts a linear array, with a rectangular footprint, which is a very common

configuration for a phased array. Arrays can be arranged as a matrix to provide more

beam control over a surface cross section, or as circular arrays which provides a more

spherical focusing pattern.

A phased array transducer is functionally categorized by type, frequency, number of ele-

ments and size of elements. Considering these characteristics, the following can be said:

� Most phased array transducers are angle beam type, designed for use with either

a plastic wedge or a straight plastic shoe (zero degree wedge) or delay line. Direct

contact and immersion transducers are other available types.

� Most ultrasonic flaw detection is done between 2 MHz and 10 MHz, so most phased

array transducers fall within that range. Lower and higher frequency probes are

also available. As with conventional transducers, penetration increases with lower

frequency, while resolution and focal sharpness increase with higher frequency.

� Phased array transducers most commonly have from 16 to 128 elements, with some

having as many as 256. A larger number of elements increases focusing and steering

capability, and can increase area coverage as well, but also increases both probe

and instrumentation costs. Each of the elements is individually pulsed to create the

wavefront of interest.

24

Chapter 3. General principles of phased arrays

Figure 3.7: Different element patterns

� As element width gets smaller, beam steering capability increases, but large area

coverage will require more elements at higher cost.

3.5 The applied delays

Giurgiutiu defined together with Bao [8] and Yu [10] two different ways for defining the

applied delays. Both ways assume M sensors (PWAS) with each PWAS acting as a point

wise omni-directional transmitter and receiver. The first way makes use of a parallel ray

approximation. This approximation is only possible in the far field. As shown in figure 3.8,

the propagating wavefront in the near field is curved and the wave his propagation direction

vary with the PWAS locations. Thus the wave propagation direction varies from PWAS

to PWAS and individual direction vectors need to be assigned to each PWAS. The second

way of defining the phased arrays makes use of the sensor locations in radial coordinates.

Also phase steering for a network of sensors is possible with this approach.

25

Chapter 3. General principles of phased arrays

Figure 3.8: Wave fronts in near field (a) and far field (b) of a PWAS array

3.5.1 1-D PWAS configuration

For a uniform linear array of M sensors (PWAS) with each PWAS acting as a point wise

omni-directional transmitter and receiver, the interspacing between the different sensors

is t, which is assumed to be much smaller than the distance r to a generic, far-distance

point P. Since t << r, the rays joining the sensors at a point P seems to be parallel for this

point. Because of the array spacing, the distance between one PWAS and the generic point

P will be different from the distance between another PWAS and P. For the m-th PWAS,

the distance will be shorted by m(t cos(ϕ)). If all the PWAS are fired simultaneously, the

signal from the m-th PWAS will arrive at P quicker by ∆m(ϕ) = m(t cos(ϕ))/c with c the

propagation speed of the signal. If the PWAS are not fired simultaneously, but with some

individual delays δm,m = 0, 1, ...,M − 1, then the total signal received at point P will be:

sP (t) =1

r

M−1∑m=0

sT (t− r

c+ ∆m(ϕ)− δm) (3.1)

where 1/r represent the decrease in the wave amplitude due to the omni-directional 2-D

radiation, and r/c is the delay due to the travel distance between the reference PWAS

(m = 0) and the point P. Beam steering towards an angle ϕ0 with an array of M omni-

directional sensors is achieved when δm = ∆m(ϕ0) such that equation 3.1 becomes:

sP (t) = M1

rsT (t− r

c) (3.2)

26

Chapter 3. General principles of phased arrays

i.e. an M times increase in the signal strength with respect to a simple sensor.

Figure 3.9: Uniform linear array of M omni-directional sensors

3.5.2 2-D PWAS configuration

The PWAS phased array is developed by using the delay-and-sum algorithm and by using

the exact wave propagation paths. Combined with PWAS Lamb wave principles, the

beamforming consists of two steps:

1. Applying delay δm and weight wm to the propagating wave from the m-th PWAS,

f(~rm, t)

2. Summing up the output signals of the total of M PWAS

This two-step procedure can be mathematically expressed as

z(~r, t) =M−1∑m=0

wmf(~rm, t− δm) (3.3)

The delays can be adjusted to focus the array his maximum output beam on a particular

propagating direction while the weighting factors can be used for further beam enhance-

ment, such as changing the beam his shape of reducing sidelobe levels.

A coordinate system with its origin coinciding with the phased center is used. As illustrated

in figure 3.10, the target P (r, ϕ) is ~rm away from the m-the PWAS located at ~sm. The

following notations are used as well: ~ξ as the unit direction vector from origin O to the

target P, ~ξm as the unit direction vector from the mth PWAS to P and ~km = ~ξm · ω/c.

27

Chapter 3. General principles of phased arrays

Figure 3.10: Coordinate system with O the center of the M PWAS

The wave front at the target P from the m-the PWAS is

f(~rm, t) =1√rmej(ωt−

~km·~rm) (3.4)

with normalized magnitude. The synthetic wave front at P from the total of M PWAS

then is

z(~r, t) =M−1∑m=0

wmf(~rm, t) =M−1∑m=0

wm1√rmej(ωt−

~km·~rm) (3.5)

If we normalize the quantity rm by the quantity r, rm = rm/r, formula 3.5 can be rewritten

as

z(~r, t) = f(t− r

c) ·

M−1∑m=0

wm1√rmejω( 1− ˜rm

c) (3.6)

This synthetic signal z(~r, t) is fully determined by the second multiplier (summation), which

depends on the weights wm and the normalized PWAS locations rm. To steer the output

wave front z(~r, t) towards a certain direction ϕ0, i.e. to reinforce the wave in the desired

direction ϕ0 with respect to waves propagating in other directions, the delays δm(ϕ0) are

introduced:

z(~r, t) = f(t− r

c) ·

M−1∑m=0

wm1√rmejω( 1− ˜rm

c−δm(ϕ0)) (3.7)

This equation shows that the maximum beamforming is expected if the exponential part

is equal to one meaning 1− ˜rmc− δm(ϕ0) = 0. Hence, the proper delay applied to the mth

PWAS is

δm(ϕ0) =1− rmc

(3.8)

28

Chapter 3. General principles of phased arrays

Then the synthetic signal at this particular direction ϕ0 becomes

z(~r, t) = f(t− r

c) ·

M−1∑m=0

wm1√rm

(3.9)

Further manipulation to shape the maximum beam at the desired direction ϕ0) can be

achieved by adjusting the weighting factor wm. One way is to use the factors to compensate

the difference caused by the PWAS locations by defining wm =√rm. The synthetic wave

of the M PWAS array at P is now

z(~r, t) = f(t− r

c) ·M (3.10)

It can be seen that the synthetic wave z(~(r), t) is M times reinforced of the wave coming

from a single PWAS located at the origin. This manifests that with proper delays and

weights, phased arrays are able to direct at certain direction with enhanced magnitude.

When the direction ϕ0 changes, beam steering of the PWAS phased array is accomplished

thereby.

If the target meets the far field condition, the parallel ray assumption applies. The generic

formulas can be reduced to a simplified format as described in 3.5.1.

3.6 Imaging basics

As told before, phased array systems can sweep a sound beam from one probe through a

range of refracted angles, along a linear path, or dynamically focus at a number of different

depths, thus increasing both flexibility and capability in inspection setups. This added

ability to generate multiple transducer paths within one probe adds a powerful advantage

in detection and naturally adds the ability to ”visualize” an inspection by creating an

image of the inspection zone. Phased array imaging provides the user with the ability to

see relative point to point changes and multi-angular defect responses, which can assist in

flaw discrimination and sizing. While this may seem inherently complex, it can actually

simplify expanding inspection coverage with increased detection by eliminating the complex

fixtures and multiple transducers that are often required by conventional UT inspection

methods. Some common visualising formats will now be described.

29

Chapter 3. General principles of phased arrays

3.6.1 A-Scan

Any ultrasonic instrument typically records two fundamental parameters of an echo: how

large it is (amplitude), and where it occurs in time with respect to a zero point. This

transit time in turn is usually correlated to reflector depth or distance, based on the sound

velocity of the test material and the simple relationship distance = velocity · time.

The most basic presentation of ultrasonic waveform data is in the form of an A-scan, or

waveform display, in which echo amplitude and transit time are plotted on a simple grid

with the vertical axis representing amplitude and the horizontal axis representing time.

One example can be seen in figure 3.11.

Figure 3.11: A-Scan

3.6.2 B-Scan

Another way of presenting this information is as a Single Value B-scan. A Single Value

B-scan is commonly used with conventional flaw detectors and corrosion thickness gages

to plot the depth of reflectors with respect to their linear position. The thickness is

plotted as a function of time or position while the transducer is scanned along the part

to provide its depth profile. Correlating ultrasonic data with actual transducer position

allows a proportional view to be plotted and allows the ability to correlate and track data

to specific areas of the part being inspected. In the case below, the B-scan shows two deep

30

Chapter 3. General principles of phased arrays

reflectors and one shallower reflector, corresponding to the positions of the side drilled

holes in the test block.

A cross sectional B-scan provides a detailed end view of a test piece along a single axis.

This provides more information than the single value B-scan presented above. Instead

of plotting just a single measured value from within a gated region, the whole A-scan

waveform is digitized at each transducer location. Successive A-scans are plotted over

elapsed time or actual encoded transducer position so as to draw pure cross-sections of the

scanned line. This allows visualization of both near and far surface reflectors within the

sample. With this technique, the full waveform data is often stored at each location and

may be recalled from the image for further evaluation or verification. To accomplish this,

each digitized point of the wave form is plotted so that color representing signal amplitude

appears at the proper depth.

Figure 3.12: Single Value B-Scan

31

Chapter 3. General principles of phased arrays

Figure 3.13: Cross sectional B-Scan

3.6.3 C-Scan

Another presentation option is a C-scan, a two dimensional presentation of data displayed

as a top or planar view of a test piece, similar in its graphic perspective to an x-ray image,

where color represents the gated signal amplitude or depth at each point in the test piece

mapped to its position. Planar images can be generated on flat parts by tracking data to

X-Y position, or on cylindrical parts by tracking axial and angular position. For conven-

tional ultrasound, a mechanical scanner with encoders is used to track the transducer’s

coordinates to the desired index resolution.

With phased array systems, the probe is typically moved physically along one axis while

the beam electronically scans along the other according to the focal law sequence. Signal

amplitude or depth data is collected within gated region of interest just as in conventional

C-scans. In the case of phased arrays, data is plotted with each focal law progression, using

the programmed beam aperture.

32

Chapter 3. General principles of phased arrays

Figure 3.14: C-Scan with a phased array transducer in progress

3.6.4 S-Scan

A phased array system uses electronic scanning along the length of a linear array probe

to create a cross-sectional profile without moving the transducer. As each focal law is se-

quenced, the associated A-scan is digitized and plotted. Successive apertures are ”stacked”

creating a live cross sectional view. In practice this electronic sweeping is done in real time

so a live cross section can be continually viewed as the transducer is physically moved. Be-

low is a real time image with a 64 element Linear phased array probe. In the example below

the user programmed the focal law to use 16 elements to form an aperture and sequenced

the starting element increments by one. This results in 49 individual waveforms that are

stacked to create the real time cross-sectional view across the transducer’s 1.5”length.

33

Chapter 3. General principles of phased arrays

Figure 3.15: Phased Array Linear Sectoral Scan

Of all imaging modes discussed so far, the Angular Sectoral scan is unique to phased array

equipment. In a linear sectoral scan, all focal laws employed a fixed angle with sequencing

apertures. Angular sectoral scans, on the other hand, use fixed apertures and steer through

a sequence of angles. Two main forms are typically used. The most familiar, very common

in medical imaging, uses a zero degree interface wedge to steer longitudinal waves creating a

pie-shaped image showing laminar and slightly angled defects. The second format employs

a plastic wedge to increase the incident beam angle for generation of shear waves, most

commonly in the refracted angle range of 30 to 70 degrees. This technique is similar to

conventional angle beam inspection, except that the beam sweeps through a range of angles

rather than a just single fixed angle determined by a wedge. As with the linear sectoral

scan, the image presentation is a cross-sectional picture of the inspected area of the test

piece. The actual image generation works on the same stacked A-scan principle that was

discussed in the context of linear sectoral scans introduced before. The end user defines the

angle start, end, and step resolution to generate the sectoral image. The aperture remains

constant, with each defined angle generating a corresponding beam with characteristics

defined by aperture, frequency, damping and the like. The waveform response from each

angle (focal law) is digitized and plotted related to color at the appropriate corresponding

angle, building a cross sectional image. In actuality the sectoral scan is produced in real

time so as to continually offer dynamic imaging with transducer movement. This is very

34

Chapter 3. General principles of phased arrays

useful for defect visualization and increases probability of detection, especially with respect

to randomly oriented defects, as many inspection angles can be used at once.

Figure 3.16: Phased Array Angular Sectoral Scan

3.6.5 Combined formats

Phased array images are powerful in their ability to provide real time visualization of vol-

umetric data. Through the electronic scanning process, imaging truly becomes real time

and is used in both manual and automated systems to increase probability of detection.

Especially in automated and more capable phased array instruments, the ability to display

multiple image types and store complete raw waveform information for the entire inspec-

tion allows post-scanning analysis of the inspection. Because all the ultrasonic waveform

data is collected, this post-analysis allows reconstruction of sectoral scans, C-scans or B-

scans with corresponding A-scan information at any inspection location. For example,

the screen below simultaneously displays the rectified A-scan waveform, a cross-sectional

B-scan profile, and a C-scan image of a set of reference holes in a steel test block.

Figure 3.17: Phased Array Angular Sectoral Scan

35

Chapter 4

Phased arrays in Structural Health

Monitoring

The previous chapters described the basic principles about ultrasonics and phased arrays.

Now it is time to describe how these two topics are combined for Structural Health Moni-

toring reasons. A lot of research has already been done and also today, many projects about

phased arrays are running. This chapter will describe some of the previous investigations.

4.1 Phased array sensor

Purekar and Pines [5] interrogated beam and plate structures using phased array concepts.

They investigated a plate with two free and two clamped edges as in figure 4.1. For damage

detection applications, a hole in a plate would reflect incoming waves. An array of piezo-

electric patches was placed along one of the free edges. Instead of making holes in the plate

to alter the plate structure, masses were added to the plate to disturb the wave patterns.

The middle element of the array was excited with a chirp with a bandwidth between 1000

and 8000 Hz and a duration of 0,001 s. The input chirp as well as the resulting reflections

from boundaries and simulated damage was recorded for each piezoelectric sensor. The

undamaged signals sundami were then subtracted from the damaged signals sdami to remove

the reflections from the boundaries:

∆si = sdami − sundami for i = 1, ..., N (4.1)

The response of the array 4.2 and with this, the energy 4.3 reflected back towards the array

36

Chapter 4. Phased arrays in Structural Health Monitoring

were calculated:

ψ(ϑ, ω) = F (ϑ,∆s1, ...,∆sN) (4.2)

ψ(ϑ) =

∫ ω2

ω1

|ψ(ϑ, ω)|2 dω (4.3)

In this equations, F is an operator to construct the array response, ϑ is the angle to steer

toward and ω is the frequency of the signal.

Polar plots of this energy function vs. the steering angle ϑ(Figure 4.2) showed that the

main lobe of the array energy was pointed into the direction of the damage. To avoid more

than one main lobe within 0 ≤ ϑ ≤ π, the Nyquist criterium dx0 ≤ λ2

must be satisfied

with dx0 the element interspacing and λ the smallest wavelength under consideration.

Figure 4.1: Phased array on a plate

Figure 4.2: Normalized ψ(ϑ) with a mass located at 100° (left) and 130° (right)

37

Chapter 4. Phased arrays in Structural Health Monitoring

4.2 Embedded-Ultrasonic Radar algorithm

Giurgiutiu and Bao [8] verified that Lamb waves can be satisfactorily generated and de-

tected with PWAS, that the signal is transmitted omni directionally and that the signals

are strong enough and attenuation is sufficiently low for echoes to be detected. Giurgiutiu

and Bao developed a phased array technology for thin wall structures (e.g., aircraft shells,

storage tanks, large pipes, etc.) that uses Lamb waves to cover a large surface area through

beam steering from a central location. They defined the Embedded-Ultrasonic Structural

Radar (EUSR) algorithm. This algorithm is based on two general principles:

1. Guided Lamb waves are generated by Piezoelectric Wafer Active Sensors (PWAS).

These waves stay confined inside the walls of a thin-wall structure and hence can

travel over large distances

2. Conventional phased-array radars assume a uniform linear array of M sensors with

each PWAS acting as a pointwise omni-directional transmitter and receiver

The algorithm uses the pulse-echo method. Each element of the array sends a transmitted

smooth-windowed tone-burst of duration tP with an appropriate time-delay. The received

signal to be analyzed has a duration t0 and starts at tP . With this, the time of flight delay

τTOF is calculated.

Figure 4.3: Uniform linear array of M omni-directional sensors (PWAS) spaced at pitch d

As explained in chapter 3, constructive interference for the direction φ0 is achieved if the

applied delay δm on each sensor is equal to δm = m(d cosφ0)/c, m = 0, 1, ..,M − 1. Then

the total signal received in P (r, φ0) is an M times boost of the original signal:

sP (t) = M1

rsT (t− r

c) (4.4)

38

Chapter 4. Phased arrays in Structural Health Monitoring

At the target, the signal is backscattered with a backscatter coefficient A. Hence, the total

received signal in the array when the appropriate time delays are applied, is:

sR(t) =A ·M2

R2

M−1∑m=0

sT (t− 2R

c) (4.5)

For the practical implementation, one active sensor at a time is activated as transmitter.

The reflected signals are received at all the sensors and with them, the synthetic beam-

forming responses 3.2 are formed. As in general the crack location is not known, the target

angle φ0 needs to be determined. This is done by using an azimuth sweep technique, in

which the beam angle φ0 is modified until the maximum received energy is obtained:

max ER(φ0) =

∫ tP+t0

tP

|sR(t, φ0)|2 dt (4.6)

If the target direction φ0 is found, the actual round-trip time of flight,τTOF , is calculated

using the cross-correlation between the received and the transmitted signal.

y(τ) =

∫ tP+t0

tP

sR(t) · sT (t− τ)dt (4.7)

The estimated τTOF = 2R/c is attained where this function reaches his maximum. Hence,

the estimated target distance R can be calculated. So, the target angle and distance is

known and the target location is fully defined.

Figure 4.4: The basis of pulse-echo method: (a) transmitted smooth-windowed tone-burst; (b)received signal to be analyzed

39

Chapter 5

Simulation of phased array wave

propagation

A program was developed to understand better the wave propagation of the phased array.

The program defines a three dimensional array: K x K x t with K the number of divisions

on the plate in the X and Y direction and t the number of time intervals. The origin of

the plate is considered to be in the down left corner of the plate. The ultimate goal is

to study the possibilities of a phased array for sending a signal. With this program, the

constructive and destructive interferences of the waves can be made visible. A Graphical

User Interface, GUI, was made to see more easily the influences of the different parameters.

The first part of this chapter describes the program. The second part of this chapter shows

some interesting figures and investigates the influence of some parameters.

5.1 Program description

The propagation of Lamb waves was simulated. Because this project involves an aluminum

plate, the dispersion curves in aluminum were studied to find the propagation speed of the

waves. A propagation frequency of 100 kHZ is used here in a plate with 2 mm thickness.

As can be seen on the dispersion curves in figure 2.6, the group velocity of S0 is 5440 m/s

when the frequency thickness product is 100 kHz · 2 mm = 0.2 MHz ·mm.

40

Chapter 5. Simulation of phased array wave propagation

5.1.1 Hanning window

The actuators are actuated with an excitation signal. This signal is a Hanning window-

signal because of the following reasons:

� The reflections of the boundaries and cracks do not interfere with the actuation

signal.

� It results in a better Fourier spectrum.

The same function as in [6] is used:

a(t) = A0 sin(ωA(t− ϕ)) · sin(ωA10

(t− ϕ)) (5.1)

with A0 the wave amplitude, ωA = 2π100 kHz and ϕ the applied time delay.

Because Matlab can only work with discrete variables, it is necessary to define first a time

array. The time array and the hanning window are programmed at the same time. The

signal has a duration of 5 times the smallest period under consideration.

time = zeros(300);

a = zeros(300);

for t = 2 : 300

time(t) = time(t− 1) + deltaT ime

if ϕ ≤ time(t) and time(t) ≤ ϕ+ 5 · TAa(t) = A0 sin(ωA(t− ϕ)) · sin(ωA/10(t− ϕ))

end

end

Figure 5.1: Hanning window

41

Chapter 5. Simulation of phased array wave propagation

5.1.2 Radial propagation of the signal

The signal will propagate radially with a velocity equal to the group velocity. The program

calculates for each point the radial distance (R) to the actuator in (X,Y). With this distance

and the group velocity c, the time the signal needs to reach this point is calculated (B).

The scale of the simulation is incorporated by multiplying R with delta ·10−3, the distance

in mm between two adjacent points in the matrix created. If the actual time is bigger than

B, the signal in this point is calculated using the actuation signal with a time delay equal

to a conversion of B to an integer number. Damping is applied by use of the damping

function exp(−εR) with ε being the damping factor initially set to be 0,07.

F = zeros(k, k, int);

for x = 1 : k

for y = 1 : k

for t = 1 : int

R =√

(x−X)2 + (y − Y )2

B = R ∗ delta ∗ 10−3/c

if B ≤ time(t)

D = round(B/deltaT ime)

F (y, x, t) = a(t−D)

end

end

end

end

with F(y,x,t) the resulting amplitude of the wave in point (x,y) at a time t and c the

propagation speed of the S0 waves.

5.1.3 Primary boundary reflections

Mathematically Lamb waves are a circle with center in the actuator growing with time.

When a part of that circle arrives to a boundary, it is reflected symmetrically in the opposite

direction. For the left boundary reflection the time the signal generated in actuator (X,Y)

needs to arrive to the boundary, is called Tleft. If the actual time is bigger than this time,

the reflections are calculated. First the area under influence is defined: the Y-component

varies from Ymin until Ymax and the X-component varies from 1 until Dist, where the

42

Chapter 5. Simulation of phased array wave propagation

distance is defined by using the equation of a circle. In a similar way, the primary reflections

from the upper, down and right border are obtained.

Dleft = x;

T left = Dleft/c ∗ delta ∗ 10−3;

Racc = time(t) ∗ c/(delta ∗ 10−3);

if time(t) > Tleft

H = sqrt(Racc2 −Dleft2);yMin = round(Y −H);

yMax = round(Y +H);

for y = yMin : yMax

Dist = round(abs(X − sqrt(Racc2 − (y − Y )2)));

for x = 1 : Dist

R = sqrt((Dleft+ x)2 + (Y − y)2);

B = R ∗ delta ∗ 10( − 3)/c;

D = round(B/deltaT ime);

Fleft = A(t−D) ∗ exp(−εR);

end

end

end

5.1.4 Phase delays

The phase delays used for beamsteering are equal to (m− 1) · d · δ · 10(−3)/c · cos(ϕ0). In

this formula, d is the interspacing of the actuators and ϕ0 is the angle the beam is sent

too. This angle is defined as can be seen in figure 4.3.

5.1.5 Graphical User Interface

In order to study the influence of the different parameters, a Graphical User Interface, GUI,

was implemented. This Graphical User Interface consists of different blocks, each defining

a particular part of the Lamb wave propagation. The initial settings are in accordance

with a plate of 1,5 m x 1,5 m x 2 mm and an excitation frequency of 100 kHz.

� Hanning window input - This block describes the Hanning window by means of

the amplitude and two frequencies f. They define the Hanning window as follows:

a(t) = Amplitude · sin(2π Frequency 1 · t) · sin(2π Frequency 2 · t) (5.2)

43

Chapter 5. Simulation of phased array wave propagation

� Lamb wave propagation - The propagation speed of the signal is equal to the

group velocity. The group velocity depends on the Lamb wave mode and of the

excitation frequency as can be seen in figure 2.6. This GUI simulates the S0 and the

A0 Lamb wave modes. Some frequency-thickness products are predefined.

� Damping - The damping coefficient ε and the damping function can be varied.

� Actuators - The number of actuators can be chosen and for each actuator the

position needs to be defined. It is also possible to work with different scales. The

interspace between two points in the grid is equal to delta mm. In accordance with

a plate of 1,5 m x 1,5 m the number of elements in the X and Y-direction goes from

1 to k.

� Phase delays - The phase delays can be calculated using a steering angle or can be

manually defined.

� Plots - Three plots will be generated during the program execution. Each of these

plots can be defined in three ways. The first way is to generate the grid and define

a colourmap of the amplitudes in each point at a certain time. Another way is by

giving the time signal in one actuator and the last way is by giving the time signal

in a predefined point.

44

Chapter 5. Simulation of phased array wave propagation

Figure 5.2: Graphical User Interface

5.2 S0 wave propagation

5.2.1 One actuator

To control the radial propagation of the signal, one point was actuated with the Hanning

window. This sensor is at position (750,750). In figure 5.3 it can be seen that points at

the same distance of this point, have the same amplitude. So it is proved that the signal

propagates radially. The radial movement of the different peaks can also be noticed.

45

Chapter 5. Simulation of phased array wave propagation

Figure 5.3: Radial propagation of signal with one actuator: (a) at time 0,0000625 s, (b) alongx = 750

5.2.2 Three actuators

Three sensors were placed in a network configuration to see the signal interferences. The

actuators their position is as follows: (34, 60), (50, 32) and (66, 60). Figure 5.4 shows that

the places with constructive interference change all the time.

Figure 5.4: Three sensors in a network configuration

5.2.3 Seven actuators

All the actuators have the same distance from the southern boundary and are symmetric

to the middle of the plate. The signal is directed toward direction 60º. After some time,

the constructive interference becomes visible as can be seen in figure 5.5. Two directions

46

Chapter 5. Simulation of phased array wave propagation

of constructive interference can be noticed. To know if this is due to grating lobes, the

actuator interspacing is studied. This interspacing has to be smaller than half the wave-

length. In this case, the wavelength is 26,5 mm and the interspace is 40 mm. It can be

concluded that grating lobes are present.

Figure 5.5: Signal propagation with seven actuators

Some parameters were changed to see their influence. At first, the influence of the actu-

ator interspacing was studied (figure 5.6). It can be seen that the area with constructive

interference is best defined for an interspacing of 20 mm. Next simulations will be made

using this interspacing.

The next parameter that was changed was the steering angle. This was done to see if the

delays are defined well. As can be seen in figure 5.7, the angle is well defined.

5.3 Total wave propagation, primary reflections in-

cluded

With one actuator, the signal looks like 5.8. The S0 wave propagates the fastest and

the A0 follows later. The time signal in sensor 3 with actuator 2 is now compared with

experimental obtained data [6]. It can be seen that the arrival of the wave packages is in

good agreement with the program but the amplitude of the signals are not good. A better

damping function will be generated in chapter 7.

47

Chapter 5. Simulation of phased array wave propagation

Figure 5.6: Variation of interspacing with seven actuators

Figure 5.7: Variation of steering angle with seven actuators

48

Chapter 5. Simulation of phased array wave propagation

Figure 5.8: Total wave propagation with reflections: (a) at time 1,045 ms, (b) comparisonbetween programmed and experimental obtained result

The steering with seven actuators is again simulated. This gives figure 5.9. There are

several areas of constructive interference. The Nyquist criterium is different for the S0 and

A0 mode. For the S0 mode, with a propagation speed of 5440 m/s, the sensor interspacing

has to be smaller then 54 mm. For the A0 mode, with a propagation speed of 2300 m/s,

the sensor interspacing has to be smaller then 23 mm. So, this criterium is fulfilled for

both Lamb wave modes. The delays applied are in accordance with the S0-speed as it is

expected that the amplitude of this wave package will be bigger then the amplitude of the

A0 wave package. Experiments later will verify if there is something like wavelength-based

tuning (see 2.6.1) and according to this the obtained time signals will be verified.

Figure 5.9: Seven actuators steered to 50° using S0 velocity, different interspacing: (a) 7.5 mm,(b) 15 mm, (c) 20 mm

49

Chapter 6

Numerical simulations

Up till now, the wave propagation was made visible by a self-created program. In this

chapter, it is tried to obtain the same results with a Finite Element Program. The program

used in this work is the commercially available finite-element program ANSYS. Because

the displacement equations in 2.5 are very complicated, various displacements were tried.

In the end, it was possible to simulate a radially propagating signal. The signal applied

(6.1) was the same signal as used in [6]. The signals obtained there were used as reference

signals.

A · sin(2πf · t) · sin(2πf/10 · t) (6.1)

6.1 Element

The element chosen to use in the numerical simulations was SHELL63. This element has

both bending and membrane capabilities. Both in-plane and normal loads are permitted.

The element has six degrees of freedom at each node: translations in the nodal x, y, and

z directions and rotations about the nodal x, y, and z axes. Stress stiffening and large

deflections are included.

The geometry, node locations and the coordinate system for this element are shown in figure

6.1. The element is defined by four nodes, four thicknesses, an elastic foundation stiffness,

and the orthotropic material properties. Orthotropic material directions correspond to the

element coordinate directions. For the next simulations, the parameters were specified as

in table 6.1.

50

Chapter 6. Numerical simulations

Figure 6.1: SHELL63 geometry

Material thickness 2 mm

Young’s modulus E 70e9 Pa

Poisson’s ratio ν 0,35

Density 2700 kg/m3

Isotropic

Table 6.1: Parameter specifications

6.2 Simulated Z displacement

At first, a Z-displacement in the node of actuation was simulated. The time signals were

generated for a period of 1 ms. In figure 6.2, some radial propagation of the signal can be

estimated. When looking at figure 6.3, the propagation of the wave can not be noticed but

it can be seen that the signal propagates radially.

51

Chapter 6. Numerical simulations

Figure 6.2: Simulated Z-displacement in actuator 1: (a) XY-plot, (b) Z-displacement in sensor2, (c) Z-displacement in sensor 3

Figure 6.3: Simulated Z-displacement in actuator 1

6.3 Simulated Y displacements in 2 nodes above each

other

Next an Y displacement was simulated in two nodes up to each other. The lower one had

a negative Y displacement and the upper one a positive Y displacement. Again the radial

52

Chapter 6. Numerical simulations

propagation was studied (figure 6.4). It can be seen that the signal is not propagating

exactly radially. Nevertheless the propagation of the initially applied wave can be seen.

Figure 6.4: Simulated Y-displacement in 2 adjacent nodes

6.4 Simulated displacements in 4 adjacent nodes

To obtain a better radial propagation of the signal, displacements were applied to four

adjacent nodes of the intended actuated node P. A positive Y displacement was applied

above P, a negative Y displacement under P, a positive X displacement to the right of P

and a negative X displacement to the left of P. The signals in points at an equal distance

of P were investigated (figure 6.5). Radial wave propagation can be noticed because the

first wave package arrives at the same time. The boundary reflections are also visible and

arrive for each point at a different time.

6.5 Simulated displacements in 8 adjacent nodes

Some test with a simulated displacement in 8 nodes adjacent to the intended actuated

node P was also performed to see if this gives a better radial propagation. The simulated

53

Chapter 6. Numerical simulations

Figure 6.5: Simulated displacements in 4 adjacent nodes to the actuator: signals obtained in 4points at an equal distance

displacement can be seen in figure 6.6. The accuracy of the last two methods is now verified

by the reference signals (figure 6.7). Also a test was done with simulated displacements in

16 nodes around P. The results are not good. The results obtained with 8 and 16 adjacent

nodes do not show the different wave packages clearly. The results obtained with 4 adjacent

nodes show different wave packages but there is a problem with timing: in sensor 1 the

signal arrives too late and in sensor 3 the signal arrives too early. As can be seen, there is

no influence of the applied amplitude. Normally, a signal with amplitude 10−6 is applied.

When a signal with amplitude 1−6 is applied, the signal gets 10 times smaller but the

signals have the same shape.

Figure 6.6: Simulated displacements in 8 adjacent nodes to the actuator: (a) simulated dis-placements, (b) signals obtained in 4 points at an equal distance

54

Chapter 6. Numerical simulations

Figure 6.7: Results from numerical simulations and experimental results, actuator 2

55

Chapter 7

Experimental results

This chapter describes the experimental obtained results. The constructive interference

when actuating a signal in more then one actuator is verified. Also some remarks are made

that will be important for future work.

7.1 Experimental setup

The experimental setup consists of an aluminum plate and some piezoelectric wafers. By

use of cables, a NI Expresscard-8360 and a Data Acquisition Unit NI PXI-1333 with 9

outputs and 4 inputs, information is passed between a laptop and the transducers. In

the laptop, a oscilloscope and a function generator are simulated in LABVIEW. The os-

cilloscope is a NI PXI-5105 and the function generator is a NI PXI-5421. Everything

together simulates a PXI (PCI eXtensions for Instrumentation) environment. PXI is a

rugged PC-based platform for measurement and automation systems. PXI combines PCI

electrical-bus features with the rugged, modular, Eurocard packaging of CompactPCI, and

then adds specialized synchronization buses and key software features. PXI is both a high-

performance and low-cost deployment platform for measurement and automation systems.

[1]

The experiments are performed in the laboratory of robotics in the university. This is a

very large laboratory where a lot of people constantly are working on different projects.

During the experiments, no attention was payed to sounds from machines, people talking,

or any other noise, even knowing that all these influence the piezoelectric wafers. This

creates a non-controlled environment. As the ultimate goal is to use the transducers in

56

Chapter 7. Experimental results

Figure 7.1: The equipment and plate in the laboratorium

flight, where there are a lot of external influences, there is no need to use a controlled

environment.

The aluminum plate under investigation is a square plate of 1, 5 m x 1, 5 m and 2 mm thick-

ness. The experiments made use of two plates. One was a damaged one with three sensors

in a network configuration. This plate had two cuts: one of size 20 mm x 1 mm and paral-

lel to the northern and southern boundary (first cut) and the other of size 40 mm x 1 mm

and perpendicular to the direction transducer 1 - transducer 2. The second plate under

investigation is a non-damaged plate. This plate was instrumented with an array of four

transducers and two control transducers. The origin of the plates is considered to be in

the down left corner, the plate is considered to be in the XY-plane with the Z-as coming

out of the plate. The coordinates of the transducers can be found in table 7.1.

Network Array

x (mm) y (mm) x (mm) y (mm) x (mm) y (mm)

1 1125 750 1 712 45 4 787 45

2 750 375 2 737 45 C1 750 750

3 375 1125 3 762 45 C2 300 588

Table 7.1: Coordinates of the transducers

57

Chapter 7. Experimental results

Figure 7.2: Plates under investigation: (a) Damaged plate with network of transducers, (b)Non-damaged plate with array of transducers and two control transducers

Figure 7.3: Some details of the setup: (a) array on plate, (b) cable connections

58

Chapter 7. Experimental results

7.2 First series of experiments

The first experiments were done on the damaged plate with a network of transducers. The

actuation signal used is:

a(t) = sin(ωAt) · sin(ωA10t) (7.1)

with ωA = 2πf kHz. At first, the new equipment was verified with a frequency f =

100 kHz. Later, different frequencies were tried to see the influence of the frequency on

the signal. Each of the transducers was used once as an actuator while the other transducers

were used as sensors. The frequencies under investigation are: 50 kHz, 100 kHz, 125 kHz,

150 kHz, 175 kHz, 200 kHz, 300 kHz and 400 kHz. The wave package has every time a

duration of half the period of the signal used i.e. 5/f .

7.2.1 Verification new equipment

Because the first experiments were done with a similar setup as in [6] but with new equip-

ment, the signals obtained with the new equipment needed to be verified. The new ex-

periments were executed on the plate with the two cuts. As can be seen in figure 7.4, the

signals are in good agreement. There is a difference in amplitude but this is due to a bigger

multiplication factor used in the present experiments.

Figure 7.4: Comparison between results obtained with actuator 1 and sensor 2: (a) old equip-ment, (b) new equipment

59

Chapter 7. Experimental results

7.2.2 Variation of frequency

As Lamb waves are dispersive, the group velocity varies with frequency. For each frequency,

the velocity of the S0 and A0 Lamb wave modes can be found in the dispersion curves 2.6.

The distance between the sensors is known, so the arrival of the direct wave package can

be calculated. When the wave arrives at a boundary, it is supposed that the wave is

reflected symmetrically in the opposite direction. With this, also the distance the wave

has to travel to arrive in a sensor after he is reflected from one of the boundaries can be

calculated. Results can be seen in 7.2. The wave packages from actuator i arriving in

sensor j need to travel the same distance as the wave packages from actuator j to sensor i.

Now, all arrival times can be calculated. As an example, the arrival time of the different

wave packages for a frequency of 100 kHz is given in the table 7.3 and 7.4. The wave

package leaves the sensor after a time equal to 5/f so also the departure times can be

known. With this information, the signals obtained in the sensors can be understood. The

wave packages are indicated in figures 7.5 and 7.6. S0 and A0 stand for the arrival of the

direct wave, respectively S0 and A0. If there is a letter adjusted between brackets, it means

the arrival of a primary reflection. The letters used are s, n, e and w and they are standing

for respectively south, north, east and west. It can be seen in the figures below that the

wave packages are best visible with a frequency between 100 kHz and 200 kHz.

Actuator sensor Direct Reflection s Reflection n Reflection e Reflection w

1 2 530,33 1185,85 1912,13 1185,85 1912,13

1 3 838,53 2019,44 1352,08 1546,16 1546,16

2 1 530,33 1185,85 1912,13 1185,85 1912,13

2 3 838,53 1546,16 1546,16 2019,44 1352,08

3 1 838,53 2019,44 1352,08 1546,16 1546,16

3 2 838,53 1546,16 1546,16 2019,44 1352,08

Table 7.2: Traveling distance of wave packages from one actuator to one sensor

60

Chapter 7. Experimental results

Actuator 2 to sensor 1

Wave S0 time (s) A0 time (s)

Direct 9,8e-5 2,31e-4

Reflection south 2,18e-4 0,515

Reflection north 3,51e-4 0,831

Reflection east 2,18e-4 0,515

Reflection west 3,51e-4 0,831

Table 7.3: Arrival time of wave packages in sensor 1

Actuator 2 to sensor 3

Wave S0 time (s) A0 time (s)

Direct 1,54e-4 3,65e-4

Reflection south 0,371e-3 0,878

Reflection north 0,248e-3 0,588

Reflection east 0,284e-3 0,672

Reflection west 0,284e-3 0,672

Table 7.4: Arrival time of wave packages in sensor 3

Figure 7.5: Influence on frequency on obtained signal in sensor 1 with actuator 2

A study was done of the amplitude of the direct S0 and A0 wave package. Between the

arrival and departure time of a wave package, the maximum amplitude of the signal can be

61

Chapter 7. Experimental results

Figure 7.6: Influence on frequency on obtained signal in sensor 3 with actuator 2

considered as the amplitude of that wave package at the distance between the actuator and

the sensor. Sometimes there is an overlap between the different wave packages and then

the amplitude was neglected. For this, data is missing about the amplitude of the A0 wave

package at low frequencies. This study was done for all three actuators and gave similar

results for all of them. Figure 7.7 shows the results with actuator 1. It can be seen that the

A0 amplitude follows a similar pattern as the S0 amplitude but at a lower amplitude. For

this, it can be imagined that there is no wavelength-based tuning as referred to in 2.6.1.

Attenuation can be noticed between the S0 amplitude at 0, 533 m and 0, 839 m.

Figure 7.7: Variation of the amplitude of the S0 and A0 wave package with frequency, actuator2 actuated

62

Chapter 7. Experimental results

7.2.3 Damping function

To avoid the excitation of a resonance signal, experiments were done with a signal of

200 kHz. As can be seen in figure 7.7, the amplitude of the signal varies with frequency

and with distance. In this part, an appropriate damping function will be defined for a

signal of 200 kHz. This function is only dependent of the distance from the actuator. This

damping function will be based on the points mentioned in table 7.5:

Distance (m) S0 amplitude A0 amplitude

0 1 1

0,53033 0,08786 0,032018

0,83853 0,05784075

1,18585 0,046308

1,35208 0,0336665

Table 7.5: Wave amplitude in function of distance from the actuator

The following damping functions were tried:

� (R/1000)2

� (R/1000)5/2

� (R/1000)3

� (R/1000)(10/3)

� a polynomial trendline (degree 6) through the keypoints, given by Excel

R is the radial distance (in m) from the actuator. In the end, it was concluded that a

damping function of (R/1000)10/3 was the best for the S0 propagation and (R/1000)2 for

the A0 propagation. To obtain the right amplitude, the damping function has to be divided

by thirty. This is the multiplication factor used for the oscilloscope. Results with actuator

2 can be seen in figure 7.8.

7.3 Second series of experiments

It can be seen in figure 7.7 that the amplitude functions reach a maximum around 150 kHz.

This suggests the existence of a natural frequency there. To verify this, some pulses were

63

Chapter 7. Experimental results

Figure 7.8: Final comparison with adapted damping function: (a) sensor 1 - actuator 2, (b)sensor 3 - actuator 2

64

Chapter 7. Experimental results

applied to the actuator and the power spectra of the received signals were investigated.

One of these power spectra can be seen in figure 7.9. The frequencies where the maximum

occurs, are noted and can be found in table 7.6. The average is 143,4 kHz and this is

considered as the natural frequency of the system.

Figure 7.9: Power spectrum of the signal in sensor C1

Test Frequency (kHz)

1 146

2 144

3 154

4 132

5 136,8

6 147,6

Average 143,4

Table 7.6: Natural frequency

7.4 Third series of experiments

On the damaged plate with a network of transducers, two transducers were used as actu-

ator. The signal in the third transducer, used as a sensor, is supposed to be the sum of

the signal received there with each of the actuators separately. Results with a frequency of

150 kHz can be seen in figure 7.10. It was calculated that the biggest difference between

the experimental obtained result and the sum of the two signals is about 5%.

65

Chapter 7. Experimental results

Figure 7.10: Results with two actuators, signals taken in sensor 2: (a) experimental results, (b)programmed results

7.5 Fourth series of experiments

The following series of experiments was done on the non-damaged plate with four actuators.

The constructive interference in the sensor in the area with constructive interference was

noticed. Furthermore it was tried to find an optimal actuating function. Together with

the different functions, the influence of the frequency was investigated.

7.5.1 Constructive interference with the array

A simulation was done of the propagation of the signal with four actuators. This simulation

showed (figure 7.11) that the area with constructive interference is in front of the array.

Because C1 is located in front of the array, a stronger signal should be encountered in

C1 then in C2. Focus for the constructive interference is payed to the direct S0 wave

package which arrives at first in the sensors and has no problems with overlap with primary

66

Chapter 7. Experimental results

reflections. In figure 7.12, it can be seen that an array of two actuators already has some

constructive interference. With an array of four actuators, the constructive interference is

even bigger.

Figure 7.11: Programmed propagation of the signal: (a) 0,00007 s, (b) 0,0001 s

Figure 7.12: Constructive interference of the array: (a) signals in C1, (b) signals in C2

7.5.2 Influence of more actuators: internal impedance

Each PWAS transducer has an internal impedance. When using more then one actuator,

the internal impedance of the total system changes. This can be noticed when looking

at the power spectra of the actuator. For this test, one output of the PXI-1333 unit is

linked with one PWAS and with one input of the same unit. By use of some electrical

67

Chapter 7. Experimental results

linking components (see figure 7.3(b)), other PWAS are also coupled with the signal. The

amplitude of the spectra goes down with the number of actuators as can be seen in figure

7.13. When interpreting the experimental results, this may not be forgotten.

Figure 7.13: Influence of more actuators

7.5.3 Different actuation signals

The influence of some other signals was studied. These signals are given some names to

simplify the following discussion:

� signal 1: sin(2πft) · sin(2πf10t)

� signal 2: sin(2πft) · 12(1− cos(2πf

5t))

� signal 3: sin(2πft) · 12(1− cos(2πf

5t))2

� signal 4: sin(2πft) · 12(1− cos(2πf

5t))1/2

For each of these signals the power spectrum is calculated (figure 7.15). In the previous

described experiments, signal 1 is used. By looking at the signals, signal 3 seems to be a

better signal because it has a slower beginning and ending. Nevertheless it has the lowest

power response. Signal 1 and signal 4 look very similar. Also their power spectrum is in

good agreement. Signal 2 has nothing special and no more attention will be payed to it.

68

Chapter 7. Experimental results

Figure 7.14: Signals studied: (a) signal 1, (b) signal 2, (c) signal 3, (d) signal 4

Up till now it is not clear which signal will give the best results. Some experiments on

the non-damaged plate were done to give more information. These experiments were done

with a frequency of 80 kHz, 140 kHz and 200 kHz and with the four actuators of the

array actuated. The experiments showed that the signal in C2 has a lot of noise when

applying a signal of 80kHz to the actuators (figure 7.16). This figure also proves that the

signal is stronger in C1 than in C2. The wave packages received in C1 with an actuation

signal of 200 kHz are a little bit better defined then the one received with an actuation

signal of 140 kHz although the amplitude of the signal is bigger with an actuation signal

of 140 kHz. This because 140 kHz is about the natural frequency of the system.

To go on with the study about the signals, a view was taken to the signals in C1 with

140 kHz and 200 kHz and with signal 1, 3 and 4. As signal 1 and 4 are very similar, also

the received signals with this signals are very similar. Received signals from signal 3 have

some moments where there is almost no noise and so, the wave packages are a little bit

better defined.

69

Chapter 7. Experimental results

Figure 7.15: Power spectrum of the different signals

Finally, the multiplication factor amplitude S0 C1amplitude S0 C2

is now studied for signal 1, signal 3

and signal 4 with frequencies of 140 kHz and 200 kHz. Results are noted down in table

7.7. The multiplication factor is the biggest for signal 3. It should be mentioned that the

differences are not so big.

140 kHz 200 kHz

signal 1 6,362 6,451

signal 3 6,619 6,738

signal 4 6,362 6,547

Table 7.7: Multiplication factor

Finally it can be concluded that signal 3 with 140 kHz will give the best results. Because

of the excitation frequency of 140 kHz, the received signals will have a big amplitude which

make them easy to distinguish from noise. Furthermore, the obtained signals from signal

3 have some moments without noise so the different wave packages can be discovered more

easily. Signal 3 also has the biggest multiplication factor concerning the arrival of the

direct S0 wave.

70

Chapter 7. Experimental results

Figure 7.16: Received signals with signal 3: (a) 80 kHz in C1, (b) 80 kHz in C2, (c) 140 kHzin C1, (d) 140 kHz in C2, (e) 200 kHz in C1, (f) 200 kHz in C2

7.6 Fifth series of experiments

With the equipment used, it is not immediately possible to apply delays. To make some

steering of the area with constructive interference possible, the polarisation of the piezo-

electrics was changed by changing the connections. In figure 7.18, the propagation of the

signal is predicted. As told before, when the four actuators have the same polarisation, the

signal has constructive interference in front of the array. When A1 and A4 are actuated

with an opposite polarisation, the areas with constructive interference are not well defined.

This because the interspace is too big and grating lobes are present. When A2 and A3

are actuated with an opposite polarisation, the area with constructive interference is quite

big. When the four actuators are actuated and the last two have an opposite polarisation,

71

Chapter 7. Experimental results

Figure 7.17: Received signals in C1: (a) signal 1, 140 kHz, (b) signal 1, 200 kHz, (c) signal 3,140 kHz, (d) signal 3, 200 kHz, (e) signal 4, 140 kHz, (f) signal 4, 200 kHz

the areas with constructive interference are best defined. For this reason, the connections

of the A3 and A4 transducer were changed on the plate.

In figure 7.19, experimental results with signal 3 at a frequency of 200 kHz are shown.

When focusing on the S0 mode, it is known that this mode arrives in the sensors after

a time of 130, 6µs and leaves them 25µs later. With the four actuators there is a strong

constructive interference as told before. The signal in C2 is only a little bit stronger when

the polarisation of A3 and A4 is changed. This is because C2 is not exactly in the area of

constructive interference as can be seen in figure 7.18. The constructive interference in C2

can be noticed in the results obtained with a different polarisation of A1 and A4 and with

a different polarisation of A2 and A3 because in this case, C2 is in the area of constructive

interference.

72

Chapter 7. Experimental results

Figure 7.18: Influence of polarisation, visualisation of signal at 0,00014 s: (a) four actuatorswith same polarisation, (b) A1 and A4 with different polarisation, (c) A2 and A3with different polarisation, (d) A1 and A2 with different polarisation then A3 andA4

Figure 7.19: Experimental results: (a) signals in C1, (b) signals in C2

73

Chapter 8

Conclusions and further research

8.1 Obtained results

The program written was verified by experiments. Now, the behavior of a phased array

of PWAS transducers can be simulated. Steering of the signal was proved and a better

damping function was obtained for a particular frequency (200 kHz). An interface was

made to see the influence of the different parameters faster.

The experiments were done with new equipment. This equipment gives the same results

as with the equipment used before but is more stable. By varying the frequency, it was

found that there is no wavelength-based tuning as found in the literature. The S0 and A0

Lamb wave mode have a similar variation in amplitude. A natural frequency of 143, 4 kHz

was found for the system under investigation.

The constructive interference with two actuators was shown. It was in good agreement with

the programmed results. Because no phasing of the signals was possible, the polarisation of

some actuators was switched. The constructive interference was predicted by the program

written and later, it was seen that the amplitude of the S0 mode was stronger in the control

sensor in the area of the constructive interference.

8.2 Future work

The program written works well but for small grids and long time simulations, it needs a

lot of time. Concerning the damping function, more tests has to be done to find a proper

74

Chapter 8. Conclusions and further research

damping function as the one used in this project is based on only a few points at a quite

long distance from the actuator.

Concerning the simulation with a finite element program, other ways of simulating a radial

propagating signal need to be studied. There is also a possibility to work with an extended

version of ANSYS or with another program, that can simulate piezoelectric behavior.

The experiments for this thesis were done with an array of four actuators. With an array

of more actuators, stronger interference will be possible. Up till now, it was not possible

to apply a specify delay to the actuators. Methods to make this possible need to be

investigated and tested. This methods will make use of microelectronics. For this reason

it may be interesting to involve someone with more electrical knowledge in the project.

The final goal of this investigation, is to use phased arrays for Structural Health Monitoring.

For this, also cracks should be simulated with the program. Instead of making real cracks

in the plate, one should think of another way of simulating damage in order not to make

long-life damages to the plate. An algorithm should be thought of to investigate the plate

and make the cracks possible in a time-efficient manner.

75

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77