THE STUDY AND DEVELOPMENT OF ENERGYHARVESTING VIBRATION ABSORBERS

Ryan L. Harne; Advisor: Ricardo A. BurdissoDepartment of Mechanical Engineering. Virginia Polytechnic Institute and State University.

131 Durham Hall (MC 0238). Blacksburg, VA, 24061. USA. Phone: (540) 231-4162. Email: rharne@vt.edu

Vibrational energy harvesting seeks to convert ambient en-ergy into electricity when battery replacement or line trans-mission is infeasible or impracticable. Electromechanicalmass-spring harvesters are designed to exhibit a resonancefrequency close to the principal vibrational frequency of themain or environmental system; excited near to resonance,the harvesters convert the kinetic or potential energy intoelectricity by means of the electromechanical coupling mech-anism. Passive vibration control research has historicallyconsidered the mass-spring system as a lightweight means bywhich to attenuate structural vibration. This research seeksto unify the objectives of energy harvesting and structuralpanel vibration control by the study and development of en-ergy harvesting vibration absorbers (EHVA) capable of con-currently satisfying both goals. New challenges are imposedin adopting this perspective, namely the dynamic couplingof the EHVAs to the host structure and the development ofversatile devices which balance both objectives. Numericalmodeling shows that the objectives are not in direct opposi-tion and experimental results show that careful EHVA designand employment adequately meet both goals.

1 IntroductionThe employment of remote sensor systems to monitor

the health of structures has inadvertently led to the problemof powering such devices in environments far removed frompractical line transmission or battery replacement. In recentdecades, there has been significant development towards har-nessing wind, solar and geothermal energy which could beused to power such remote networking systems. However,some environments lack these resources as a consistent sup-ply but contain ever-present levels of ambient vibration. Infact, this vibration may be the very reason for monitoring thestructure’s fatigue degradation.

As a result, vibrational energy harvesting has become arecent topic of research with the overall aim of convertingthis ambient energy source into electricity by means of elec-tromechanical devices [1,2]. Electromechanical mass-spring“harvesters” are designed such that they exhibit a natural fre-quency close to the dominant frequency of ambient vibration,for instance bridge vibrations; the harvesters resonate whenapplied to the structure and convert a portion of this kinetic

and potential energy into electrical power by means of theelectromechanical coupling. The necessary power require-ment for each distributed sensor is relatively low, typicallyon the order of µW or mW, and a number of early harvesterprototypes have been found to satisfy this goal. Research hasfocused on piezoelectric cantilevered beam harvesters [3–5]and electromagnetic oscillators [6–8] in particular due to thehigh electromechanical coupling which is possible depend-ing on the system scale. In general, energy harvesting re-search has afforded greater focus to the modeling and designof prototypes assuming that the available energy resource tobe harvested is infinite. Therefore, it is often the case that theharvesters are assumed to be of negligible inertial influencerelative to the host vibrating system [9–12].

From a different perspective, vibration control researchhas long studied and exploited electromechanical mass-spring-dampers for the purposes of adaptive, tunable ac-tive vibration suppression [13–15]. This approach actuatesthe devices via the electromechanical coupling to enhancethe passive vibration control capability of the mass-spring-dampers. Thus, vibration control research has utilized elec-tromechanical mass-spring systems for the “actuation” ca-pability of the devices while energy harvesting research hasfocused on the “sensing” capability of the devices.

Since both fields utilize the same device but for differ-ent purposes, it appears logical to attempt a unification ofgoals: vibration control with energy harvesting. Some stud-ies have recently begun to consider this possibility: shuntdamping induced by piezoelectric energy harvesting to at-tenuate UAV wing flutter [16–18]; self-powered magneto-rheological damper systems for vehicle suspensions [19–21];skyscraper energy harvesting tuned-mass-dampers [22–24].The present research adopts the perspective of the latter ref-erenced works: that of studying and developing energy har-vesting vibration absorbers (EHVA). The target vibrationcontrol problem is to attenuate structural panel vibrationswhich are primarily low in frequency and consist of the low-est structural modes. The benefit in converting this energyinto electricity as opposed to mechanically dissipating it is toreduce the necessity for power transmission cabling to sen-sors which are oftentimes mounted onto or near to structuralpanels, for example in aerospace, maritime or other transport

Harne 1

00.2

0.40.6

0.8

00.2

0.40.6

0.81

Tra

nsve

rse

defle

ctio

n

y, m x, m

(a)

(1,1) mode

1

00.2

0.40.6

0.8

00.2

0.40.6

0.81

Tra

nsve

rse

defle

ctio

n

y, m x, m

(b)

(3,1) mode

Fig. 1. Low order modal vibration of a simply-supported panel. (a)(1,1) mode. (b) (3,1) mode.

vehicles typically loaded with monitoring electronics.The objectives of this paper are to summarize the devel-

opment of a distributed piezoelectric EHVA. The device de-sign, geometries and manufacture are first introduced. Next,a model of the device is presented which stems from a varia-tional method that is much more computationally efficient toutilize than exactly-defined finite element (FE) models. Fi-nally, experiments carried out with the EHVA are consideredwhich show the potential of the device to simultaneouslysuppress structural vibrations while converting a portion ofthe absorbed energy into electrical power.

2 EHVA description2.1 Device design and construction

The primary troublesome vibrations to attenuate onstructural panels are those which are induced by the lowestorder modes of the surface when excited by forces, trans-mitted waves or acoustic-structure interaction. As such, thevibration is uniquely distributed over the structural surface.Figure 1 shows an example of the (1,1) and (3,1) modes ofa simply-supported panel, showing the greater concentrationof oscillatory displacement near to the panel center. Thus,to attenuate distributed vibration, it is required to apply dis-tributed treatments to the surfaces.

A distributed and active vibration control device hadbeen briefly studied in the past but treated analytically asa distributed single degree-of-freedom (SDOF) device [25].This device was activated by the use of piezoelectric filmwhich served as the distributed spring layer. Taking the de-sign as a basis for the present work, an EHVA was devel-oped and is shown in Figure 2 in an exploded view. A dis-tributed mass layer (a thin plate) is attached to a distributedspring layer. The spring layer is composed of a circularlycorrugated and etched piezoelectric film which is bounded

top mass layer (thin plate)

non-poled PVDF film

non-poled PVDF film

etched piezoelectric film withtwo pairs of electrode leads

Fig. 2. Exploded view of the EHVA: distributed mass layer and thedistributed spring layer (corrugated piezoelectric film) bounded bytwo non-poled PVDF sheets.

Tensile bending strainCompressive bending strain

At downward position ofSDOF resonance response

(b)

Poled PVDF filmSurface electrodes

(a) Mass layer

Non-poledPVDF film

Fig. 3. (a) Undeformed cross-sectional geometry of circularly corru-gated piezoelectric spring layer with exaggerated electrode thicknessand arbitrary top mass layer. (b) Illustrated cross-sectional responsewhen top mass layer is displaced downward during SDOF resonantvibration.

via thin epoxy lines to two non-poled PVDF film sheets.The piezoelectric film, being very thin (about 20 to 100 µmin thickness) may be transversely compressed by the masslayer. For a given EHVA mass and spring design there existsa frequency of excitation at which the mass layer oscillatesin rigid-body translation compressing and stretching the cor-rugated spring beneath it, Figure 3. This is the SDOF reso-nance frequency of the device for which the EHVA outputsmaximum electrical power as well as is most capable of pas-sively attenuating structural vibrations.

At the EHVA resonance, bending strain is induced in thecircularly corrugated piezoelectric film, Figure 3 (b). It isassumed that the strain-displacement relation is linear sincerealistic oscillations of the mass layer are a small fractionof the total thickness of the corrugated spring for excitationlevels corresponding to typical vibrations of panels. Thus,the bending strain varies linearly through the thickness ofthe corrugated spring and changes sign on a given piezoelec-tric film surface electrode every half-wavelength of the cor-rugated length. It is for these reasons that the electrodes areetched prior to corrugation, such that the etched lines cor-respond to the undeformed middle-plane of the spring (see

Harne 2

etching lines along corrugated piezoelectric film

Fig. 4. EHVA corrugated and etched piezoelectric spring showingthe removal of the surface electrodes every half-wavelength to sepa-rate the electrode surfaces having opposite induced bending strain.

Fig. 5. EHVA sample having 12 full periods (wavelength 12.7 mm)of the etched and corrugated piezoelectric film.

Figure 2) and each electrode surface contains regions of in-phase strain. Finally, this process yields two electrode pairoutputs which may be combined out-of-phase to maximizethe net voltage output and thus maximize the harvested elec-trical energy. Figure 4 shows a close-up photograph of afinal EHVA sample with the etching of the piezoelectric filmapparent within the distributed spring. Figure 5 shows a pho-tograph of a full sample.

2.2 Mechanical and electrical dynamicsTo evaluate the mechanical and electrical dynamics of

the device when excited near to the SDOF natural frequency,EHVA samples were manufactured and attached to a shakerplatform for testing. Figure 6 shows the shaker test setup inwhich the device is excited in the transverse direction so as toobserve the mechanical and electrical dynamics referencedfrom the input acceleration. The acceleration frequency re-sponse function (FRF) is computed as the ratio of the topmass acceleration to the shaker table acceleration; the volt-age FRF is the ratio of the voltage across the harvester loadresistance, R1, with respect to the input acceleration.

One sample having piezoelectric film thickness, ts =28 µm, corrugation wavelength, λ= 12.7 mm and mass layerarea density of 12.38 kg/m2 was tested and the resulting ac-celeration and voltage FRFs are given in Figures 7 and 8,respectively. Around 118 Hz, the device is found to resonatesuch that the mass layer oscillates in rigid-body transla-tion compressing and stretching the corrugated piezoelectricspring. Maximum voltage output therefore also occurs at thisfrequency. Minor electromechanical coupling is observed toinfluence the frequency or damping at resonance; such cou-pling is more apparent for piezoceramic-based (PZT) energyharvesting prototypes in which a notable damping and fre-

White noisegenerator, 50-400Hz

Shaker

Accelerometer

Laservibrometer

R1

Stiff shakerplatform

vp

Fig. 6. Shaker test setup to evaluate EHVA acceleration and voltageFRFs.

50 100 150 200 250 30015

10

5

0

5

10

15

20

25

30

Frequency, Hz

Acce

l. TF

mag

nitu

de, d

B re

f. 1.

0 m

/s2

110 115 120 12518

19

20

21

22

23

24

25

26

Frequency, Hz

Acce

l. TF

mag

nitu

de, d

B re

f. 1.

0 m

/s2

R=2kR=180kR=390kR=560k

R=2kR=180kR=390kR=560k

Fig. 7. EHVA sample acceleration FRF for variety of load resis-tances, R1.

quency shift is seen at resonance for different external cir-cuit conditions due to the higher electromechanical couplingfactors for PZT harvesters [2].

Figure 9 plots the average power across the harvesterload resistance, P = |vp|2/2R1, at the EHVA resonance for alarge range of load resistances for an input excitation of 1 g(9.81 m/s2). This is the average amount of power that couldbe harvested from a vibrating structure for this device whenthe base excitation level is around 118 Hz at 1 g. The deviceis found to output a maximum power FRF of 55.4 mW/g2 ata load resistance of R = 560 kΩ. This is comparable withmany other harvester prototypes in the literature which uti-lize more highly coupled piezoelectric materials [3–5].

A second EHVA sample was tested having similar con-struction to the prior but a greater mass area density of13.21 kg/m2. The time domain response of the electrical out-put from each electrode pair is plotted in Figure 10 at the de-vice’s resonance frequency of 100 Hz for a load resistance ofR1 = 150 kΩ and excitation level of 1.45 g (14.2 m/s2). Theelectrode pairs are observed to output equal-in-magnitudeand out-of-phase voltages, which validates the assumptionthat the bending strain changes sign every wavelength which

Harne 3

50 100 150 200 250 30010 1

100

101

102

103

Frequency, Hz

Volta

ge T

F m

agni

tude

, V/g

R=10kR=100kR=220kR=560kR=1M

Fig. 8. EHVA sample voltage FRF for variety of load resistances,R1.

103 104 105 10610 1

100

101

102

Load resistance,

Pow

er T

F m

agni

tude

, mW

/g2

At 117 HzAt 118 Hz

Max. 55.4 mW/g2

at 118 Hz, R=560k .Data taken fromshaker accel of 1 g(9.8 m/s2).

Fig. 9. EHVA sample power FRF for variety of load resistances, R1.

justified the electrode etching. Furthermore, subtracting thetwo signals maximizes the net output, best for harvestingpurposes, while combining them directly produces destruc-tive interference which cancels the signals entirely. Lastly,the response is observed to be linear for this high excitationlevel; this indicates that the EHVA elastic and electric re-sponse will be linear for amplitudes of vibration falling wellwithin the range of ambient levels considered in energy har-vesting applications [26–28].

3 EHVA electromechanical modeling3.1 Modeling formulation

For brevity, a synopsis of the modeling formulation willbe provided. Greater detail on the general mathematical ap-proach may be found in Refs. [29, 30] while the specificutilization for the present geometry and electromechanics isgiven in Ref. [24].

The objectives of modeling the present EHVA are: to as-sist in further development of the device; to optimize designparameters for maximum achievement of vibration controland energy harvesting; and to serve as a foundation for a

240 260 280 300 320 340 360 380 400

−0.1

−0.05

0

0.05

0.1

0.15

Time, ms

Voltage,V

#1#2

(b)#2+#1

#2–#1

240 260 280 300 320 340 360 380 400

−0.1

−0.05

0

0.05

0.1

0.15

Time, ms

Voltage,V

(a)

Fig. 10. Measured time series of EHVA sample electrical responseat resonance. (a) Individual electrode outputs and (b) sum and differ-ence of the two signals.

Fig. 11. Structural panel excited by external point forces to whichare attached continuously distributed piezoelectric vibration controldevices.

rigorous evaluation of the EHVA capability to achieve bothgoals simultaneously. At present, a linear electric-elastic for-mulation is employed which serves to solve for the responseof the device under typical excitation encountered in struc-tural panel vibration control concerns or energy harvestingapplications.

The geometry under study is an arbitrarily bounded,rectangular structural panel excited by point forces, Fig-ure 11. To the panel are attached a number of distributedpiezoelectric vibration control devices, composed of a dis-tributed mass layer and distributed electric-elastic springlayer. The electromechanical coupling induced via the com-pression of the piezoelectric spring layer is assumed to beonly related to transverse (z-axis) compression, and the re-sulting electrical potential is attached to an external circuitmodeled as a simple load resistance, R1. Elastic characteris-tics of the spring layer are determined via the combination ofsuperposition and homogenization methods available in theliterature [31–33]. Continuity of displacement and transversestress between the distributed spring and the two boundingplates allows the displacements of the spring to be expressedin terms of the top and bottom plate displacements, reducingthe number of unknowns.

Assuming harmonic response and applying Ritz methodsolutions for the base plate displacements having generalized

Harne 4

co-ordinates mb (ω), top plate displacements having general-ized co-ordinates mt (ω) and induced circuit voltage vp (ω),the governing equations of the coupled electric-elastic sys-tem are determined [24]:

1

R10 0

−Θs,t Kt +Ks,t Ks,b−Θs,b Ks,t Kb +Ks,b

(1)

+ jω

Cp ΘTs,t ΘT

s,b0 Ct +Cs,t Cs,b0 Cs,t Cb +Cs,b

−ω2

0 0 00 Mt +Ms,t Ms,b0 Ms,t Mb +Ms,b

vp(ω)

mt(ω)mb(ω)

=

00

F(ω)

where matrices K, C, M and Θ are the stiffness, damping,mass and electromechanical coupling terms, respectively; Cpis the capacitance of the piezoelectric film; and matrices hav-ing subscript (s, i) with i = b, t indicate components ascribedto the spring layer written in terms of the base plate, b, orthe top plate, t, displacements. Those marked by ˜( ) indi-cate elastic coupling terms due to the spring layer. Note thatelectromechanical coupling is due to the spring layer; yet,because the spring layer mechanical displacements are writ-ten in terms of the base and top plate responses, the couplingis seen to directly affect the host structural vibration as wellas the response of the top mass layer of the vibration controland energy harvesting device.

Solution to Eq. 1 is carried out for each frequency, ω, todetermine the dynamics of the base plate, the dynamics of thetop plate, and the resulting voltage in the harvesting circuit.Metrics of present interest for prediction are the accelerationFRF, voltage FRF and spatial-average mean-square panel ve-locity. As earlier, average electrical power is computed asP(ω) = |vp (ω) |2/2R1.

3.2 Experimental validation of the modelThe EHVA shown in Figure 12 was produced using

piezoelectric film having characteristics as given in Ref. [24].Both surface electrodes were carefully etched as per the de-sign of Figure 2 using a fine-tipped watercolor brush and fer-ric chloride solution. Afterwards, the film was constrainedusing thin lines of quick-drying epoxy and facing sheets ofnon-poled PVDF film into the circularly corrugated formhaving 5 full periods. Evident in Figure 12 are the lead at-tachments connected to the etched surface electrodes notingthat four connections are required given the four unique seg-ments of the electrode after etching. Elastic homogenizationtechniques were used to determine equivalent orthotropicthick plate elasticity parameters to characterize the springlayer stiffness matrix, cE

s [31–33]. These equivalent materialproperties are given in Ref. [24]. The transverse parameter,Ez, is many orders of magnitude less than the cross-planarbending stiffnesses, Ex and Ey, and there is no coupling be-tween them, vyz = vxz = 0. This indicates that transverse dy-namics of the layer are similar to a layer of vertical springs,

Fig. 12. Photograph of EHVA using a circularly corrugated piezo-electric film as the distributed spring layer. Electrical leads are alsoshown to be attached to the etched surface electrodes of the film.

Fig. 13. Comparison of modeled and measured acceleration FRFmagnitudes for EHVA for various load resistances, R1.

as per [33,34], not coupled to the remaining dynamics of thelayer.

The device was fixed to a stiff shaker table platform forFRF testing. The drive acceleration used during the test was14.2 m·s−2 (1.45 g). In the model, the base plate was as-sumed to have free boundary conditions and be excited bya centrally-located unit point force. For FRF computation,(x1,y1) = (0,0) and (x2,y2) = (0,0).

A comparison of the measured and modeled accelerationFRF is given in Figure 13 for four values of load resistance,R1. The EHVA is observed to exhibit a principal SDOF reso-nance, akin to a 1D mass-spring-damper system. For smallervalues of R1, the natural frequency occurs at approximately78.5 Hz; as the resistance is increased, the coupling throughthe piezoelectric material produces a stiffer distributed springlayer and increases the resonance to the open circuit value(i.e. R1 → ∞) at approximately 81.5 Hz. This is a substan-tial shift in frequency for a piezoelectric material having suchlow electromechanical coupling as compared with, for exam-ple, piezoceramics. However, this may be due to the circu-larly corrugated design which induces relatively high bend-ing strain in the film as the mass oscillates vertically at res-onance. The model almost exactly predicts the locations ofthese resonant frequencies for various load resistances butmeasurements exhibited uniformly more roll-off above reso-nance. This lapse in the model may be explained by employ-ing too great of a loss factor for the equivalent spring layerelastic material properties.

Harne 5

Fig. 14. Comparison of modeled and measured voltage FRF mag-nitudes for EHVA for various load resistances, R1.

It is also noted that there is no noticeable shunt dampingeffect due to dissipation in the electrical circuit. The inertialinfluence of the top mass layer dominates dissipative circuiteffects. Therefore for this particular specimen the dampingof the device is mostly a function of the elastic characteris-tics of the PVDF film itself as opposed to electromechanicalcoupling.

Figure 14 compares the measured and predicted voltageFRF for the sample. The model fairly accurately predicts theamplitude and shifting resonance frequency of the voltageFRF resonance. Similar to past work in piezoelectric energyharvesting [35], the voltage FRF is measured and predictedto both increase in overall amplitude as well as in frequencyas the load resistance of the energy harvesting circuit is in-creased.

4 Experimental study of EHVA performance4.1 Panel experiment description

A simply supported panel was used for testing an EHVA.The panel itself was a part of a larger mounted structure withthe panel extending off of the structure by means of thinshims to replicate simple supports as closely as possible. Themechanical and geometric information of the panel and theEHVA top mass layer are provided in Ref. [24]. It was ob-served that the edges of the panel support were not exactlyclassical simple supports but additionally constrained the ro-tation of the edges. This was compensated for in the model-ing by including additional edge stiffnesses in computation.This is achieved by assuming the edge is further constrainedby rotational springs as described in Refs. [36, 37]. How-ever, due to the inexact boundaries along the edges of the testpanel, it was not possible to perfectly match eigenfrequencypredictions of the panel with those measured.

The mounted structure and the panel were both sus-pended as shown in Figure 15 with a test schematic shownin Figure 16. An electrodynamic shaker was attached to abored hole at the center of the panel through a short stinger.The shaker input was bandpass filtered white noise from 50–800 Hz. A PCB 208 A03 force transducer was positioned be-tween the stinger and the panel. An array of thirty PCB 330A

Fig. 15. Photograph of simply supported panel in mounted structurewith EHVA attached to the top surface. The shaker, stinger, forcetransducer and accelerometer array are connected to the undersideof the panel from the photograph perspective.

(a)

(b)(c)

(d)(e) (f)

(g)(h)

(j)

Fig. 16. Panel test setup schematic: (a) panel; (b) bandpass filteredwhite noise; (c) shaker; (d) force transducer; (e) accelerometer arraydistributed over full bottom surface of panel; (f) EHVA attached totop panel surface; (g) external load resistance; (h) voltage acrossresistor; (j) data acquisition and processing system.

accelerometers were randomly positioned on the undersideof the panel, with the top surface left clear for later applica-tion of the piezoelectric device. The global accelerance TFwas computed as the square root of the ensemble average ofthe squared accelerance TFs between each accelerometer andthe force transducer.

The piezoelectric spring layer design was the same asfor the earlier sample. The device was much larger than thespecimen used in FRF testing of Section 3.2 and included12 periods of the circular corrugation. However, despite thelarger size, the mass ratio of the EHVA relative to the mass ofthe panel was only µ = 0.0104, or just over 1%. In practicalterms, this is an unusually lightweight device to employ forvibration control purposes but also meets the general objec-tive in energy harvesting of attaching devices of negligibleinertial influence to the host structure. The SDOF naturalfrequency of the device was predicted by the model to be ap-proximately 94 Hz. This was very close to the (1,1) mode ofthe simply supported panel which was measured and com-puted to be 97.5 Hz.

Harne 6

4.2 Experimental results and model comparisonThe panel accelerance TF was initially measured with

nothing attached to the top surface. Afterwards, the cen-ter of the EHVA was attached at (93,0) mm relative to thepanel center. The device was attached by means of a thindouble-sided tape. The tests were repeated varying the loadresistance, R1, in the energy harvesting circuit to which theelectrical leads from the etched electrodes were attached.The out-of-phase voltages from the electrodes were appro-priately combined so as to yield the maximum electrical sig-nal. The untreated panel accelerance TF and that with theapplied piezoelectric device are shown in Figure 17 compar-ing predicted results and measurements when the externalresistance was R1 = 180 kΩ.

The model very closely predicts the untreated panel re-sponse with the exception of the location of some reso-nances. This is attributed to the inexact simply supportedboundary conditions of the panel. It is apparent that the con-nection of the shaker to the panel is not exactly at the panelcenter since several of the asymmetric modes are excited,for instance the (2,1) mode at 186 Hz. After observation ofthis feature, the model was appropriately adjusted to simu-late the point force excitation at (4,4) mm relative to panelcenter. The two lowest-order symmetric panel resonances—the (1,1) mode at 97.5 Hz and the (3,1) mode at 350 Hz—arethoroughly excited by the shaker and these are the resonancesfor which the piezoelectric device was designed and appro-priately positioned. The ideal position for attenuating thesemodes was to place the device at the panel center but thiswas not achievable due to interference from the shaker con-nection.

Following application of the EHVA, the panel vibrationof the (1,1) mode is observed to be significantly attenuated.The resonance at 97.5 Hz is predicted to be suppressed byapproximately 20 dB and the measurements show a simi-lar amplitude of attenuation. Two split-resonances at 87 and100 Hz are generated by application of the reactive device.This is a dynamic ascribed to conventional 1D vibration ab-sorbers [13] and is seen to also be the case for the distributedsystem of interest. This further exemplifies the reactive na-ture of the piezoelectric device in suppressing the panel re-sponse. The (3,1) panel resonance at 350 Hz is attenuatedby more than 10 dB but this is not due to the direct “tuning”of the device for this frequency. Instead, the suppression ofthe symmetric (3,1) mode is achieved by the mostly centralplacement of the device on the panel surface. Over the band-width of frequencies computed, the model is in close agree-ment with the measurements, despite minor misalignment ofpanel resonances due to the inexact simple supports.

For a load resistance of R1 = 180 kΩ, the power TF mag-nitude is shown in Figure 18. For the two symmetric modesin this bandwidth—(1,1) at 97.5 Hz and (3,1) at 350 Hz—the measurements show very clear maxima in the electricalpower response. While the model is close in replicating themagnitude of the power around the device SDOF natural fre-quency, 94 Hz, it slightly under estimates the peak responsewhich it predicts to occur at 100 Hz, the higher of the twosplit resonances.

Measurements at 86.5 Hz observed a maximum powerTF magnitude of 3.3 mW·N−2. The power TF is not eas-ily compatible with other metrics in energy harvesting liter-ature, more often quoted as power FRFs with units W·g−2

or simply as power at a given exciting acceleration level.Thus, the panel was instead excited only at 86.5 Hz. Themeasured average electrical power was then 0.441 µW (peakvoltage of 0.3986 V) while the drive acceleration at the panelcenter (shaker attachment) was measured to be 3.29 m·s−2

(0.335 g). This low amplitude of measured power also sug-gests the film is strained within a linear range given anotherstudy in the literature which employed piezoelectric film andachieved power levels on the order of mW [38].

Figure 18 also shows that electrical response for the de-vice when excited by panel asymmetric modes yielded strayelectrical signals, and thus the noisy response observed be-tween 120 and 320 Hz. The model does not take into accountthe precise geometry of the circularly corrugated spring layerand, instead, predicts a precipitous electrical signal drop inthis bandwidth, greater than 7 orders of magnitude. Since itis not feasible to measure such a range in electrical response,the measured noisy electrical output is justified.

Figure 19 plots the measured panel response around the(1,1) mode for a variety of load resistances, R1. Changingthe load resistance is observed to influence the magnitude ofthe vibration suppression around the (1,1) mode. This sug-gests that the larger piezoelectric vibration control device, incontrast to the much smaller sample used in FRF testing, ex-hibits enough electromechanical coupling through the manypiezoelectric corrugations to take advantage of shunt damp-ing effects in the energy harvesting circuit.

What is perhaps more interesting, however, is the effecton the panel response measured for the higher of the two splitresonances, at 100 Hz. For low R1, this resonance occurs at99 Hz. Increasing load resistance dampens this resonanceand increases the frequency to 100 Hz. Further increasingR1 reduces the damping effect and increases the resonanceup to 101 Hz. A load resistance of R1 = 82 kΩ yields an ad-ditional 2 dB of vibration attenuation of the 100 Hz split res-onance as compared with open circuit conditions, R1 =→∞.This emulates the piezoelectric shunt damping effects char-acteristic of other more frequently studied systems like can-tilevered piezoelectric beams [39]. This also further verifiesthe analogy between the present energy harvesting deviceand an electromechanically stiffened and damped vibrationabsorber, justfiying the title EHVA.

Figure 20 plots the measured device power TF for thesame selections of load resistance. The maximum powerTF achieved from these resistances occurs for R1 = 180 kΩ:3.3 mW·N−2 at 86.5 Hz. Smaller or greater load resistancesyield reduced maximum output. It is also noted that bothobjectives are best met by nearly the same choice of R1:vibration suppression of the panel is best achieved usingR1 = 82 kΩ while energy harvesting objectives maximizepower for R1 ≈ 180 kΩ. For low to moderately electrome-chanically coupled piezoelectric harvesters, this has else-where been observed in the literature in regards to dampingof the harvester itself [40].

Harne 7

50 100 150 200 250 300 350 400 450 500 550 60020

30

40

50

60

70

80

90

Frequency, Hz

Acc

ele

rance

TF

,dB

ref.

1.0

m⋅s

−2

N−

1

Untreated panel

With device, µ=0.0104, fn≈94 HzSolid: Model

Dashed: Experiment

R1=180kΩ

Fig. 17. Comparison of modeled (solid curves) and measured (dashed curves) accelerance TF magnitudes of the panel when untreated(black plots) and with the piezoelectric device (red plots). R1 = 180 kΩ.

100 150 200 250 300 350 40010

−10

10−8

10−6

10−4

10−2

Frequency, Hz

PowerTFmagnitude,W

⋅N−2

Model

Experiment

R=180kΩ

Fig. 18. Comparison of modeled and measured electrical power TF magnitude of the piezoelectric device. R1 = 180 kΩ.

Fig. 19. Panel accelerance TF around (1,1) mode for a variety ofresistances R1.

Compared to the power TF which appears promisinggiven the order of mW, the actually observed maximum av-erage power (0.441 µW for panel center drive accelerationof 3.29 m·s−2) falls well within or below the range of manyother piezoelectric energy harvesters in the literature [28].This indicates there is a need for an improved metric ofachievable power in the event the host structure may be dy-namically influenced by the attached harvesting device. Thepower TF has been employed elsewhere in literature in a non-dimensional form when the main structure and attached har-vester are both lumped parameter systems [41]. This is a

Fig. 20. Power TF around (1,1) mode for a variety of resistancesR1.

more suitable use for the power TF given the direct relationbetween applied force, the system mass and resulting accel-eration. In contrast, forces exciting distributed systems mustaccelerate the entire structure, making for a less direct rela-tion between force and acceleration beneath a given EHVA.At present, a more explicit metric—measured average powerwhen the panel is driven at a single frequency—appears suf-ficient for immediate comparison against other harvester de-signs until an alternative metric for distributed systems maybe proposed.

Harne 8

5 ConclusionsVibrational energy harvesting has served to supply elec-

trical power to small sensor systems where disposable powersources or line transmission are impractical. In many cases,these sensors are monitoring the health of the structure whichis degraded by the vibration itself over a long period of time.A logical extension is to then utilize harvester devices ofgreater inertial influence such that they suppress the vibra-tions of the host structure, like a classical vibration absorber,while still converting a portion of the energy absorbed intoelectrical power for the sensing systems. This conceptualdevelopment follows more naturally for lighter weight struc-tural systems like aerospace, maritime or transport vehiclepanels in which case EHVAs could be properly developed todynamically influence the host structure.

An EHVA was here introduced capable of suppressingthe vibrations of structural panels while converting a por-tion of the absorbed energy into electricity. The device uti-lizes a corrugated piezoelectric distributed spring such thatthe device outputs maximum electrical power around a targetSDOF natural frequency, like a conventional energy harvest-ing device. Mechanical damping is induced via the use of thecorrugated film which is polymer-based and therefore has amoderate loss factor for energy dissipation. In this manner,the EHVA serves to supply ample vibration suppression forthe host structure given reasonable limits on the electrome-chanical energy conversion of the piezoelectric film.

A model of the device was proposed and validated byexperiments. Early investigations found that the linearityassumptions utilized in the model are valid over the rangeof ambient structural acceleration encountered in typical en-ergy harvesting studies and thus justifies the models contin-ued evaluation for EHVA development. An experimental teston a realistic vibrating panel was carried out to observe thecapability of the device to achieve both vibration control andenergy harvesting. Model predictions were in good agree-ment with the measurements and the tests show the EHVAmay achieve both objectives concurrently.

The innovative extraction of environmental energy likesolar, wind, geothermal and now vibration has proven toyield sustainable alternatives to costly disposable sources orimpractical line transmission. In the event that the structuremay be dynamically influenced to an additional advantage,an energy harvesting vibration absorber appears to serve bothends. This work studied and developed one such device suit-able for structural panel vibration suppression and energyconversion and serves as validation of the EHVA concept.

AcknowledgementThe author is grateful to the NASA–VSGC Graduate

Research Fellowship for supporting this work.

References[1] Priya, S., and D.J. Inman, e., 2009. Energy Harvesting

Technologies, first ed. Springer, New York, New York.[2] Erturk, A., and Inman, D., 2011. Piezoelectric Energy

Harvesting. John Wiley & Sons.

[3] Sodano, H., Park, G., and Inman, D., 2004. “A reviewof power harvesting from vibration using piezoelectricmaterials”. Shock and Vibration Digest, 36, pp. 197–205.

[4] Anton, S., and Sodano, H., 2007. “A review of powerharvesting using piezoelectric materials (2003-2006)”.Smart Materials and Structures, 16, pp. R1–R21.

[5] Priya, S., 2007. “Advances in energy harvesting usinglow profile piezoelectric transducers”. Journal of Elec-troceramics, 19, pp. 167–184.

[6] Williams, C., Shearwood, C., Harradine, M., Mellor,P., Birch, T., and Yates, R., 2001. “Development ofan electromagnetic micro-generator”. Circuits, Devicesand Systems, IEE Proceedings, 148(6).

[7] Beeby, S., Torah, R., Tudor, M., Glynne-Jones, P.,O’Donnell, T., Saha, C., and Roy, S., 2007. “A microelectromagnetic generator for vibration energy harvest-ing”. Journal of Micromechanics and Microengineer-ing, 17, pp. 1257–1265.

[8] Elvin, N., and Elvin, A., 2011. “An experimentally val-idated electromagnetic energy harvester”. Journal ofSound and Vibration, 330, pp. 2314–2324.

[9] Poulin, G., Sarraute, E., and Costa, F., 2004. “Gen-eration of electrical energy for portable devices com-parative study of an electromagnetic and piezoelectricsystem”. Sensors and Actuators A, 116, pp. 461–471.

[10] Beeby, S., Tudor, M., and White, N., 2006. “Energyharvesting vibration sources for microsystems appli-cations”. Measurement Science and Technology, 17,pp. R175–R195.

[11] Stephen, N., 2006. “On energy harvesting from ambi-ent vibration”. Journal of Sound and Vibration, 293,pp. 409–425.

[12] Erturk, A., 2011. “Piezoelectric energy harvesting forcivil infrastructure system applications: moving loadsand surface strain fluctuations”. Journal of IntelligentMaterial Systems and Structures, 22(17), pp. 1959–1973.

[13] Den Hartog, J., 1985. Mechanical Vibrations, fourth ed.Dover Publications, New York, NY.

[14] Sun, J., Jolly, M., and Norris, M., 1995. “Passive, adap-tive and active tuned vibration absorbers–a survey”.Journal of Vibration and Acoustics, 117, pp. 234–242.

[15] Zuo, L., and Nayfeh, S., 2005. “Optimization of the in-dividual stiffness and damping parameters in multiple-tuned-mass-damper systems”. Journal of Vibration andAcoustics, 127, pp. 77–83.

[16] Anton, S., and Inman, D., 2008. “Vibration energy har-vesting for unmanned air vehicles”. In Smart Structuresand Materials 2008: Active and Passive Smart Struc-tures and Integrated Systems II, Proceedings of SPIE6928, San Diego, pp. 1–10.

[17] De Marqui Junior, C., Erturk, A., and Inman, D., 2010.“Piezoaeroelastic modeling and analysis of a generatorwing with continuous and segmented electrodes”. Jour-nal of Intelligent Material Systems and Structures, 21,pp. 983–993.

[18] Anton, S., and Inman, D., 2011. “Performance model-

Harne 9

ing of unmanned aerial vehicles with on-board energyharvesting”. In Active and Passive Smart Structures andIntegrated Systems V, Vol. 7977, SPIE, p. 79771H.

[19] Choi, Y.-T., and Wereley, N., 2009. “Self-poweredmagnetorheological dampers”. Journal of Vibrationand Acoustics, 131, p. 044501.

[20] Kim, I.-H., Jung, H.-J., and Koo, J.-H., 2010. “Ex-perimental evaluation of a self-powered smart dampingsystem in reducing the vibrations of a full-scale staycable”. Smart Materials and Structures, 19, p. 115027.

[21] Zuo, L., and Zhang, P.-S., 2012. “Energy harvesting,ride comfort, and road handling of regenerative vehiclesuspensions”. Journal of Vibration and Acoustics, 135,p. 012345.

[22] Ni, T., Zuo, L., and Kareem, A., 2011. “Assessmentof energy potential and vibration mitigation of regen-erative tuned mass dampers on wind excited tall build-ings”. In ASME 2011 International Design Engineer-ing Technical Conferences & Computers and Informa-tion in Engineering Conference.

[23] Cassidy, I., Scruggs, J., Behrens, S., and Gavin, H.,2011. “Design and experimental characterization ofan electromagnetic transducer for large-scale vibratoryenergy harvesting applications”. Journal of IntelligentMaterial Systems and Structures, 22(17), pp. 2009–2024.

[24] Harne, R., 2012. “Concurrent attenuation of and energyharvesting from surface vibrations: experimental veri-fication and model validation”. Smart Materials andStructures, 21, p. 035016.

[25] Fuller, C., and Cambou, P., 1998. “An active-passivedistributed vibration absorber for vibration and soundradiation control”. Journal of the Acoustical Society ofAmerica, 104(3), p. 1851.

[26] Roundy, S., 2005. “On the effectiveness of vibration-based energy harvesting”. Journal of Intelligent Mate-rial Systems and Structures, 16, pp. 809–823.

[27] Reilly, E., Miller, L., Fain, R., and Wright, P., 2009.“A study of ambient vibrations for piezoelectric energyscavenging”. In POWERMEMS: International Work-shop on Micro and Nanotechnology for Power Genera-tion and Energy Conversion Applications, pp. 312–315.

[28] duToit, N., Wardle, B., and Kim, S.-G., 2005. “De-sign considerations for mems-scale piezoelectric me-chanical vibration energy harvesters”. Integrated Fer-roelectrics, 71, pp. 121–160.

[29] Meirovitch, L., 1967. Analytical methods in vibrations.Macmillan, New York, NY.

[30] Reddy, J., 1984. Energy and variational methods inapplied mechanics: with an introduction to the finiteelement method. Wiley, New York, New York.

[31] Frostig, Y., 2003. “Classical and high-order computa-tional models in the analysis of modern sandwich pan-els”. Composites: Part B, 34, pp. 83–100.

[32] Cheng, Q., Lee, H., and Lu, C., 2006. “A numeri-cal analysis approach for evaluating elastic constantsof sandwich structures with various cores”. CompositeStructures, 74, pp. 226–236.

[33] Harne, R., and Fuller, C., 2012. “Modeling of a pas-sive distributed vibration control device using a super-position technique”. Journal of Sound and Vibration,331(8), pp. 1859–1869.

[34] Frostig, Y., and Baruch, M., 1990. “Bending of sand-wich beams with transversely flexible core”. AIAAJournal, 28(3), pp. 523–531.

[35] Erturk, A., and Inman, D., 2009. “An experimentallyvalidated bimorph cantilever model for piezoelectricenergy harvesting from base excitations”. Smart Ma-terials and Structures, 18(2), p. 025009.

[36] Carmichael, T., 1959. “The vibration of a rectangu-lar plate with edges elastically restrained against rota-tion”. The Quarterly Journal of Mechanics and AppliedMathematics, 12(1), pp. 29–42.

[37] Dozio, L., 2011. “On the use of the trigonometricritz method for general vibration analysis of rectangularkirchhoff plates”. Thin-Walled Structures, 49, pp. 129–144.

[38] Granstrom, J., Feenstra, J., Sodano, H., and Farinholt,K., 2007. “Energy harvesting from a backpack instru-mented with piezoelectric shoulder straps”. Smart Ma-terials and Structures, 16, pp. 1810–1820.

[39] Karami, M., and Inman, D., 2011. “Equivalent damp-ing and frequency change for linear and nonlinear hy-brid vibrational energy harvesting systems”. Journal ofSound and Vibration, 330(23), pp. 5583–5597.

[40] Liao, Y., and Sodano, H., 2009. “Structural effectsand energy conversion efficiency of power harvesting”.Journal of Intelligent Material Systems and Structures,20, pp. 505–514.

[41] Tang, X., and Zuo, L., 2011. “Enhanced vibration en-ergy harvesting using dual-mass systems”. Journal ofSound and Vibration, 330(21), pp. 5199–5209.

Harne 10