modal analysis applications spring2002 macl

7/23/2019 Modal Analysis Applications Spring2002 MACL

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Sunday, February 23, 2003Dr. Peter Avitabile [email protected] 1

Presentation Topics

New Research Concepts

MACL Research OverviewCorrelation Applications

System Modeling Research

Force Estimation Applications

Reverse Modeling Technique - DO IT

DO IT Equations

Modal Analysis and Controls Laboratory

Mechanical Engineering Department

University of

Massachusetts

Lowell

Modal AnalysisApplications

Spring 2002

Dr. Peter Avitabile

Recent Work

MACL Lab Resources

System Modeling Applications

Structural Dynamic Modeling Tools

EMC

Chile

NRO

Dryer


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Overview of Structural Dynamic Modeling Techniques 1 Dr. Peter AvitabileModal Analysis & Controls Laboratory

Structural Dynamic Modeling Techniques

Could you explainmodal analysis

Illustration by Mike Avitabile Illustration by Mike Avitabile

and how is itused for solvingdynamic problems?

Illustration by Mike Avitabile


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Modal Analysis and Structural Dynamics

INPUT

RESPONSE

INPUT TIME FORCE

INPUT POWER SPECTRUM

OUTPUT TIME RESPONSE

BOARD

DISK DRIVE

CABINET

INDUCED VIBRATIONS

INPUT FORCE

RESPONSE

F F T I F T

FORCE

FAN INDUCEDVIBRATIONS

Modal Analysis is the study of the dynamic character of asystem which is defined independently from the loads appliedto the system and the response of the system.

Structural dynamics is the study of how structures respondwhen subjected to applied loads. Many times, in one form oranother, the modal characteristics of the structure is used todetermine the response of the system.


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How Do Structures Respond Dynamically ?

The raw time response of a structure may seemcomplicated but it is really nothing more than thelinear combination of the effects of all the modes

that are excited by the specific input

response due to a vertical bumpsuperimposed on a random excitation

high speed videoshowing drop load


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Response of a Simple Plate

Simple time-frequency response relationship

FORCE

RESPONSE

time

increasing rate of oscillation

frequency


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Measure many points on theplate simultaneously to viewthe actual response

Different deformationpatterns can be seen as theexcitation sweeps from low

frequency to high frequency


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Sine Dwell to Obtain Mode Shape Characteristics

MODE 1

MODE 2

MODE3

MODE 4


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Analytical Modal Analysis

Equation of motion [ ]{ } [ ]{ } [ ]{ } { })t(FxKxCxM nnnnnnn =++ &&&

Eigensolution [ ] [ ][ ]{ } { }0xMK nnn =


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Finite Element Models

Models used for designdevelopment

No prototypes arenecessary

Modeling assumptions

Joint design difficult to model

Component interactions aredifficult to predict

Damping generally ignored

Advantages Disadvantages


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Finite Element Models

Analytical models are developedto describe the system mass andstiffness characteristics of a

component or systemThe model is decomposed toexpress the part in terms of itsmodal characteristics - its

frequency, damping and shapes

The dynamic characteristics helpto better understand how the

structure will behave and how toadjust or improve the componentor system design


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Experimental Modal Analysis

Modal characteristics

are defined from actualmeasurements

Damping can beevaluated

Requires hardware

Actual boundary conditionsmay be difficult to simulate

Different hardwareprototypes may vary

Advantages Disadvantages

MEASURED RESPONSE

FREQUENCY RESPONSE FUNCTIONS

APPLIED FORCE

[Y]

[H]

fref1

fref2

[F]


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Experimental Modal Analysis

Measured frequency responsefunctions from a modal test canalso be used to describe the

structures dynamic properties -its frequency, damping and shapes

DOF # 1

DOF #2

DOF # 3

MODE # 1

MODE # 2

MODE # 3

h32

1 2 3

1

2

3

h33h31

1 2 3

1

2

3

h23

h33

h13

40

-60

dB Mag

0Hz 800Hz

COHERENCE

INPUT POWER SPECTRUM

FRF

AUTORANGING AVERAGING

1 2 3 4


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Experimental Data Reduction

Measured frequency responsefunctions from a modal test oroperating data can be used to

develop a model of the dynamiccharacteristics of the system


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What Are Measurements Called FRFs ?

1 2 3

8

5

2

8

0

-3

8

-7

6

A simple input-output problem

-1.0000

1.0000

RealMagnitude

Phase Imaginary

DOF # 1

DOF #2

DOF # 3

MODE # 1

MODE # 2

MODE # 3


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Digital Signal Processing Flow Diagram

Actual time signals

INPUT OUTPUT

OUTPUTINPUT

FREQUENCY RESPONSE FUNCTION COHERENCEFUNCTION

ANTIALIASING FILTERS

ADC DIGITIZES SIGNALS

INPUT OUTPUT

ANALOG SIGNALS

APPLY WINDOWS

COMPUTE FFT

LINEAR SPECTRA

AUTORANGE ANALYZER

AVERAGING OF SAMPLES

INPUT/OUTPUT/CROSS POWER SPECTRA

COMPUTATION OF AVERAGED

INPUTSPECTRUM

LINEAROUTPUT

SPECTRUM

LINEAR

INPUT

SPECTRUMPOWER

OUTPUT

SPECTRUMPOWER

CROSS

SPECTRUMPOWER

COMPUTATION OF FRF AND COHERENCE

Analog anti-alias filterDigitized time signals

Windowed time signals

Compute FFT of signal

Average auto/cross spectraCompute FRF and Coherence


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Experimental Mode Shapes From FRFs

1

2

3

4

5

6

MODE 1

1

2

3

4

5

6

MODE 2


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Experimental Mode Shapes From FRFs

The task for the modaltest engineer is todetermine the parametersthat make up the piecesof the frequency response

function

Mathematical routineshelp to determine the

basic parameters thatmake up the FRF

HOW MANY POINTS ???

RESIDUALEFFECTS RESIDUAL

EFFECTS

HOW MANY MODES ???

aij1

aij2

aij3

1

2

3

3

2

1


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Flow Diagram for Response

Why and How Do Structures Vibrate?

INPUT TIME FORCE

INPUT SPECTRUM OUTPUT SPECTRUM

f(t)

FFT

y(t)

IFT

f(j ) y(j )h(j )


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What is Operating Data ?

If an excitation is applied close to a mode, thenthat mode is excited - if not, then the responseis the linear combination of all the modes excited


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The modes of the structure act like filterswhich amplify and attenuate input excitations

on a frequency basis

INPUT SPECTRUM

OUTPUT SPECTRUM

f(j )

y(j )


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The raw time response of the structure may seemcomplicated but it is really nothing more than thelinear combination of the effects of all the modes

that are excited by the specific input

response due to a vertical bumpsuperimposed on a random excitation


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What Good is Modal Analysis ?

The dynamicmodel can beused for studiesto determine the

effect ofstructuralchanges of themass, damping

and stiffness

EXPERIMENTALMODAL

TESTING

FINITEELEMENTMODELING

MODALPARAMETER

ESTIMATION

PERFORMEIGEN

SOLUTION

DEVELOP

MODAL

MODEL

STRUCTURAL

CHANGES

REQUIRED

USE SDM

TO EVALUATE

STRUCTURAL

CHANGES

Repeatuntildesired

characteristicsare

obtained

DONE

No

Yes

STIFFNERRIB

DASHPOT

SPRING

MASS

STRUCTURAL

DYNAMIC

MODIFICATIONS


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What Good is Modal Analysis ?

Simulation, Prediction, Correlation, to name a few

FREQUENCY

RESPONSE

MEASUREMENTS

FINITE

ELEMENT

MODEL

CORRECTIONS

PARAMETER

ESTIMATION

EIGENVALUE

SOLVER

MODAL

PARAMETERS

MODAL

PARAMETERS

MODEL

VALIDATION

MASS, DAMPING,

STIFFNESS CHANGES

REAL WORLD

FORCES

FORCED

RESPONSE

SIMULATION

STRUCTURAL

DYNAMICS

MODIFICATION

MODIFIED

MODAL

DATA

STRUCTURAL

RESPONSE

SYNTHESIS

OF A

DYNAMIC MODAL MODEL


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Correlation and Updating Models

Analytical and

experimental modelsare correlated andadjusted to

FINITE ELEMENT MODEL

EXPERIMENTAL MODAL MODEL

[M] , [K] [U ] , [ ]n 2

[T ] = [U ] [U ]nu ag

[E ] = [T ] [E ]un a

MAC AND

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MAC

0

0.2

0.4

0.6

0.8

1

1.2

GUYAN

0

0.2

0.4

0.6

0.8

1

1.2

IRS

0

0.2

0.4

0.6

0.8

1

1.2

SEREP

EXP1EXP2EXP3EXP4EXP5

FEM 1

FEM 2

FEM 3

FEM 4

FEM 5

0

0.2

0.4

0.6

0.8

1

FINITE ELEMENT

EXPERIMENTAL

OR

MODESWITCHING

M A C

P O C

VECTOR CORRELATION

FINITE ELEMENT EXPERIMENTAL

Experimental Analytical

CoMAC CORTHOG

DOF CORRELATION

DOF CORRELATION

VECTOR CORRELATION

F R A C

EXPERIMENTALFINITE ELEMENT

DOF CORRELATION

VECTOR CORRELATION

R V A C

ORTHOGONALITY

provide

bettercomponentand systemmodels


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Vector tools

Degree of freedom tools

Frequency tools

EXP1EXP 2

EXP 3EXP 4

EXP 5

FEM 1

FEM 2

FEM 3

FEM 4

FEM 5

0

0.2

0.4

0.6

0.8

1

FINITE ELEMENT

EXPERIMENTAL

MODAL

ASSURANCE

CRITERIA

MATRIX

PSEUDO

ORTHOGONALITY

CRITERIA

MATRIX

OR

MODE

SWITCHING

M A C

P O C

VECTOR CORRELATION

FINITE ELEMENT EXPERIMENTAL

MODAL

ASSURANCE

CRITERIA

ORTHOGONALITY

CRITERIA

OR

Experimenta l Analytica l

COORDINATE COORDINATE

CoMAC CORTHOG

DOF CORRELATION

RESPONSE

ASSURANCE

CRITERIA

F R A C

EXPERIMENTALFINITE ELEMENT

FREQUENCY

DOF CORRELATION

VECTOR CORRELATION

VECTOR

ASSURANCE

CRITERIA

R V A CRESPONSE


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Models can be adjusted to better reflect actual measuredsystem characteristics

Joint stiffness can be more accurately identified

Simplistic modeling assumptions can be modified to reflectthe actual system

ANALYTICAL MODEL

MODELIMPROVEMENT

REGIONS

MODEL

IMPROVEMENT

REGIONS


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System Models

System models are developedfrom component models whichcan be obtained from physicalmodels, reduced models, modalmodels or measurement models

All of these methods may beused to develop a system model


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System Models

Modal ModelsModal Models Reduced ModelsReduced Models

Modal/Physical ModelsModal/Physical Models Impedance ModelsImpedance Models

FULL SPACE PHYSICAL MODEL


MODAL SPACE MODEL

MODAL SPACE MODEL

MODAL TIE MATRIX



MODAL SPACE MODEL

TIE MATRIX



CONNECTION



CONNECTION


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Hybrid/Impedance Modeling

In addition to more conventionalsystem modeling approaches,measured frequency response

functions can also be used toassemble systems and provide morerealistic boundary conditions

HYBRID MODELING

MACHINE

SYNTHESIZED FROMCONNECTION IMPEDANCE

CONNECTION IMPEDANCE

MEASURED AT MACHINE

FEM OF WORKPIECE

REFERENCE IMPEDANCESYNTHESIZED FROMFEM OF WORKPIECE

CHUCK

Hz

(m/s2)/N

dB

0 25501000 2000

0

120

100

Dof 15286 REFERENCE

Dof 15286 CALCULATED

c al c3 _x yz U NI V: 19 74 :+ Z

-70

10

-60

-50

-40

-30

-20

-10

0

5 255.75100 200

-70

10

-60

-50

-40

-30

-20

-10

0

Hz

(s2)/(kg)

dB

FEM

HYBRID


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Dynamic Force Estimation

Using both measured operating data and frequency responsefunction, estimates of the dynamic forces driving the system canbe estimated

OPERATIONALDISPLACEMENTS

FREQUENCY RESPONSEFUNCTIONS

[Y]

[H]

[F]

0 50 100 150 200 250 30010

-7

10

-6

10-5

10-4

10-3

10-2

10-1

Hz

Lbf^2

Estimated force vs reference @dof17 part4

Reference

Estimated0 50 100 150 200 250 300

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Hz

Lbf^2

Estimated force vs reference @dof7 part4

Reference

Estimated


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System Response

System response can be computedfor both linear and non-linearsystems by various methods.

INPUT TIME FORCE

INPUT SPECTRUM

OUTPUT TIME RESPONSE

OUTPUT SPECTRUM

f(t)

FFT

y(t)

IFT

f(j ) y(j )h(j )

FREQUENCY RESPONSE FUNCTION


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System Disassembly and Cascaded Targets

With a specified performance level, modification oradjustment of the system matrices is required

CAB IMPEDANCES

FRAME IMPEDANCES

COMBINEDSTRUCTURE

RESPONSE

AMI

SSO/MSSO

PHANTOM

These modified systems are then usedfor system disassembly to determinecomponent required characteristics


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System Disassembly and Cascaded Targets

Components may or may nothave elemental topology

The problemis difficult


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Recent Work - Telescopes

45m in Nobeyama, Japan & both Gemini 8m in Chile/Hawaii


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Recent Work - Computers and Peripherals

Operating and modaldata collected formassive storage

devices - 40 terabyteRobust design options


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Future Work & Job Opportunities

As equipment is designed to be lighter, quieter, more efficient,easier to manufacture, etc., there will always be structuraldynamic issues to address.

This is true in all industries and sectors - aerospace, automotive,commercial products, sporting goods equipment are just a shortlist of applications where structural dynamics plays a criticalrole in the design and analysis of equipment


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Modal Analysis & Controls Laboratory

Could you explain

modal analysis

Illustration by Mike Avitabile Illustration by Mike Avitabile

and how is itused for solvingdynamic problems?

Illustration by Mike Avitabile

modal analysis applications spring2002 macl

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