Shaker Excitation Tutorial - The Modal Shop in Modal Shaker Excitation.pdf3 Dr. Peter Avitabile...

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1 Dr. Peter Avitabile Structural Dynamics & Acoustic Systems Lab Shaker Excitation Shaker Excitation IMAC 27 - Orlando, FL - 2009 Peter Avitabile Marco Peres UMASS Lowell The Modal Shop

Transcript of Shaker Excitation Tutorial - The Modal Shop in Modal Shaker Excitation.pdf3 Dr. Peter Avitabile...

Page 1: Shaker Excitation Tutorial - The Modal Shop in Modal Shaker Excitation.pdf3 Dr. Peter Avitabile Shaker Excitation Structural Dynamics & Acoustic Systems Lab Vibration Shaker Qualification

1 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Shaker Excitation

IMAC 27 - Orlando, FL - 2009

Peter Avitabile Marco PeresUMASS Lowell The Modal Shop

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Shaker Excitation

� Overview some shaker excitation techniques commonly employed in modal testing

� Review deterministic and non-deterministic methods

� Present excitation techniques that have developed from a historical standpoint

� Present some MIMO testing information

Objectives of this lecture:

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Vibration Shaker Qualification vs Modal Shaker

Many people are familiar with vibration shakers used for qualification of equipment where specific loading is applied to replicate the actual operating environment.

This is a much different testing technique than what is done formodal testing (where high loads are not applied to the structure)

SHAKER MOUNTING TABLE

SHAKER BASE

ATTACHMENT FIXTURE

TEST ITEM

EXPANDER HEAD

SHAKER ARMATURE

SHAKER BODY

FIXTURE

DRIVER COIL

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Shaker Excitation for Modal Testing

FORCE TRANSDUCER

RESPONSE TRANSDUCER

STINGER

SHAKER

STRUCTURE UNDER TEST

Its purpose is to provide input along the shaker excitation axiswith essentially no excitation of the other directions

It is also intended to be flexible enough to not provide any stiffness to the other directions

The force gage is always mounted on the structure side of the quill

NOT ON THE SHAKER SIDE

Excitation device is attached to the structure using a long rod called a “stinger”or “quill”

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Excitation Configuration

Test Signal-random-burst Random-pseudo-random-periodic-random-Chirp

Power Amplifier

Stinger force sensor

structure

Shaker

AUTORANGING AVERAGING WITH WINDOW

1 2 3 4

AUTORANGING AVERAGING

1 2 3 4

AUTORANGING AVERAGING

1 2 3 4

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Reason for Stinger

Purpose of Stinger

�Decouple shaker from test structure

�Force transducer between stinger and structure decouple forces acting in the axial direction only

�Forces acting in any other direction will be unaccounted for creating error in the measurements

Modal Shaker

Structure

Stinger

Force GageAxial

Bending

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Possible Problems with Stinger

�Suspect increase in stiffness when stinger is at higher location

Axial stiffness Axial and bending stiffness

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Stinger Configuration with Through Hole Shaker

2-part chuck

assembly

armature stinger

Force sensor

colletMod

al E

xcite

r

Tes

t Str

uctu

re

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Common Stingers

Piano wire

Modal stinger

Threaded metal rod

Threaded nylon rod

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Common Stingers

Types of Stingers Available�Drill Rod

�Threaded Rod

�Piano Wire

�Axial stiffness provided through a preload on wire

�Essentially no lateral stiffness

�Requires shaker and test fixture to be fixed

Metal

Nylon

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Shaker Excitation

CORRECT

Force gage “divorces”the stinger/ shaker from the structure

WRONG

Stinger becomes part of the test structure

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The Overall Measurement Process

INPUT FORCE OUTPUT RESPONSE

WINDOWED OUTPUTWINDOWED INPUT

AVERAGED INPUT

POWER SPECTRUM

AVERAGED CROSS

POWER SPECTRUM

AVERAGED OUTPUT

POWER SPECTRUM

FREQUENCY RESPONSE FUNCTION COHERENCE FUNCTION

INPUT OUTPUT

WINDOWED SIGNAL

AVERAGED INPUT, OUTPUT AND CROSS SPECTRA

COMPUTED FREQUENCY RESPONSE FUNCTION AND COHERENCE

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Signal Types

Excitation techniques can be broken down into two categories:

• Deterministic Signals

• Non-Deterministic (Random) Signals

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Signal Types - Deterministic

Deterministic Signals • conform to a particular mathematical relationship

• can be described exactly at any instant in time

• response of the system can also be exactly defined if the system character is known

• swept sine, sine chirp, digital stepped sine are examples

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Signal Types – Non-Deterministic

Non-Deterministic (Random) Signals • do not conform to a particular mathematical relationship

• can not be described exactly at any instant in time

• described by some statistical character of the signal

• generally have varying amplitude, phase and frequency content at any point in time

• pure random, periodic random, burst random are examples

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Signal Types – Deterministic vs Non-Deterministic

Deterministic Signals • conform to a particular mathematical relationship • can be described exactly at any instant in time • response of the system can also be exactly defined

if the system character is known • examples :swept sine, sine chirp, digital stepped sine

Non-Deterministic (Random) Signals

• do not conform to a particular mathematical relationship

• can not be described exactly at any instant in time • described by some statistical character of the signal • generally have varying amplitude, phase and frequency

content at any point in time • examples: pure random, periodic random, burst random

Goo

d f

or

IDENTIF

ICATIO

N

of s

yste

m linea

rity

Goo

d f

or

LINEARIZ

ATIO

N

of s

light

no

nlinea

rities

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Excitation Signal Characteristics

RMS to Peak

Signal to Noise

Distortion

Test Time

Controlled Frequency Content

Controlled Amplitude Content

Removes Distortion Content

Characterizes Non Linearites

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Summary Excitation Signal Characteristics

Ref: University of Cincinnati

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Remarks on General Excitation Characteristics

The complete solution of a forced harmonic excitation will result in two parts of the response– transient part which decays with time and - the steady state part of the response

tsinmF

xx2x 02nn ω=ω+ζω+ &&&

( )1n2t

1

2

n

22

n

0

t1sineX

21

)tsin(kF

)t(x

n φ+ωζ−+⎟⎟⎠⎞⎜⎜⎝

⎛ ⎟⎠⎞⎜⎝

⎛ωωζ+⎟⎟⎠

⎞⎜⎜⎝⎛ ⎟⎠

⎞⎜⎝⎛ωω−

φ−ω=

ζω−

Steady State

Transient

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Remarks on General Excitation Characteristics

The complete solution of a forced harmonic excitation will result in two parts of the response– transient part which decays with time and - the steady state part of the response

( )1n2t

1

2

n

22

n

0

t1sineX

21

)tsin(kF

)t(x

n φ+ωζ−+⎟⎟⎠⎞⎜⎜⎝

⎛ ⎟⎠⎞⎜⎝

⎛ωωζ+⎟⎟⎠

⎞⎜⎜⎝⎛ ⎟⎠

⎞⎜⎝⎛ωω−

φ−ω=

ζω−

Steady State

Transient

0 10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

2

tsinmF

xx2x 02nn ω=ω+ζω+ &&&

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Vibrations – Convolution for SDOF Sine Excitation

Start of Sine

Steady State Reached

End of Transient

Sine input AVI

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Swept Sine Excitation

INPUT EXCITATION

OUTPUT TIME RESPONSE

Slowly changing sine signal sweeping from one frequency to another frequency

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Analog Slow Swept Sine Excitation

A slowly changing sine output sweeping from one frequency to another frequency ADVANTAGES

• best peak to RMS level • best signal to noise ratio • good for nonlinear characterization • widely accepted and understood

DISADVANTAGES • slowest of all test methods • leakage is a problem • does not take advantage of speed of FFT process

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Random Excitation

An ergodic, stationary signal with Gaussian probability distribution. Typically, has frequency content at all frequencies.

AUTORANGING AVERAGING

1 2 3 4

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Random Excitation

An ergodic, stationary signal with Gaussian probability distribution.Typically, has frequency content at all frequencies. ADVANTAGES

• gives a good linear approximation for a system with slight non-linearities

• relatively fast • relatively good general purpose excitation

DISADVANTAGES

• leakage is a very serious problem • FRFs are generally distorted due to leakage

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Random Excitation

Time signal Frequency Signal

Notice that the coherence is very poor at all frequencies

0s 1.999s

0s 1.999s

1

0Hz 400Hz

0Hz 400HzAVG: 10

FRF

COHERENCE

OUTPU

T

IN

PUT

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Random Excitation

Effects of averaging

CH1 Pwr Spec

0Hz 800HzAVG: 1

-40

-90

dB Mag

CH1 Pwr Spec

0Hz 800HzAVG: 10

-40

-90

dB Mag

CH1 Pwr Spec

0Hz 800HzAVG: 100

-40

-90

dB Mag

100

10

1

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AUTORANGING AVERAGING WITH WINDOW

1 2 3 4

Random Excitation with Hanning Window

An ergodic, stationary signal with Gaussian probability distribution. Typically, has frequency content at all frequencies.

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Random Excitation with Hanning Window

An ergodic, stationary signal with Gaussian probability distributionTypically, has frequency content at all frequencies. ADVANTAGES

• gives a good linear approximation for a system with slight non-linearities

• relatively fast • overlap processing can be used • relatively good general purpose excitation

DISADVANTAGES • even with windows applied to the measurement leakage

is a very serious problem • FRFs are generally distorted due to leakage with

(significant distortion at the peaks) • excessive averaging necessary to reduce variance on data

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0Hz 400Hz

0Hz 400HzAVG: 10

0s 1.999s

0s 1.999s

Random Excitation with Hanning Window

Time signal Frequency Signal

Notice that the coherence is very poor at resonant frequencies

OUTPU

T

IN

PUT

FRF

COHERENCE

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Random Excitation with Overlap Processing

OVERLAP PROCESSING

1 3 5 7 9

2 4 6 8 10

• used to reduce test time with pure random excitations

• Hanning window tends to weight the first and last quarter of the time block to zero and this data is not effectively used in the normal averaging process

• effectively uses the portion of the block that has been heavily weighted to zero

• overlap processing allows for almost twice as many averages with the same data when fifty percent overlap is used

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AUTORANGING AVERAGING

1 2 3 4

IFT

Pseudo Random Excitation

An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has constant amplitude withvarying phase. Note that the transient part of the signal must decay and steady state response achieved before measurements aretaken to assure leakage free FRF.

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Pseudo Random Excitation

An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has constant amplitude with varying phase. ADVANTAGES

• always periodic in the sample interval • relatively fast • fewer averages than random • frequency spectrum is shapeable

DISADVANTAGES • sensitive to nonlinearities • same excitation is used for each average

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AUTORANGING AVERAGE

1

IFT

2

IFT

AUTORANGING AVERAGE

Periodic Random Excitation

An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has varying amplitude with varying phase. Note that the transient part of the signal must decay and steady state response achieved before measurements aretaken to assure leakage free FRF.

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Periodic Random Excitation

An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has varying amplitude with varying phase. ADVANTAGES

• always periodic in the sample interval • frequency spectrum is shapable • determines a very good linear approximation of the FRF

since leakage is minimized DISADVANTAGES

• a different signal is generated for each measurement • longest of all excitation techniques except swept sine

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AUTORANGING AVERAGING

1 2 3 4

Burst Random Excitation

A random excitation that exists over only a portion of the data block (typically 50% to 70%).

NOTE: Voltage mode amplifier necessary – creates back emf effect to dampen response at end of burst

Current ~ forceVoltage ~ velocity

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Burst Random Excitation

A random excitation that exists over only a portion of the data block (typically 50% to 70%) ADVANTAGES

• has all the advantages of random excitation • the function is self-windowing • no leakage

DISADVANTAGES

• if response does not die out within on sample interval, then leakage is a problem

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0Hz 400Hz

0Hz 400HzAVG: 10

0s 1.999s

0s 1.999s

Burst Random Excitation

Time signal Frequency Signal

Notice that the coherence is very good even at resonant frequencies

Notice the sharpness of the resonances and measurement quality.

End of burst

Shaker off

Response decays exponentially

OUTPU

T

IN

PUT

FRF

COHERENCE

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Sine Chirp Excitation

A very fast swept sine signal that starts and stops within one sample interval of the FFT analyzer

AUTORANGING AVERAGING

1 2 3 4

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Sine Chirp Excitation

A very fast swept sine signal that starts and stops within one sample interval of the FFT analyzer ADVANTAGES

• has all the same advantages as swept sine • self windowing function • good for nonlinear characterization

DISADVANTAGES

• nonlinearities will not be averaged out

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0Hz 400Hz

0Hz 400HzAVG: 10

0s 1.999s

0s 1.999s

Sine Chirp Excitation

Time signal Frequency Signal

Notice that the coherence is very good.

Notice the sharpness of the resonances and measurement quality.

OUTPU

T

IN

PUT

FRF

COHERENCE

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Digital Stepped Sine Excitation

Sine waves are generated at discrete frequencies which correspond to the digital values of the FFT analyzer for the frequency resolution available. The system is excited with a single sine wave and steady state response measured. Once one spectral line is obtained, the next digital frequency is acquired until all frequencies have been measured.

AUTORANGING AVERAGE

IFT

1 2 3

AUTORANGING AVERAGE

IFT

1 2 3

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Digital Stepped Sine Excitation

Sine waves are generated at discrete frequencies which correspond to the digital values of the FFT analyzer for the frequency resolution available. The system is excited with a single sine wave and the steady state response is measured. Once one spectral line is obtained, the next digital frequency is acquired until all frequencies have been measured. ADVANTAGES

• excellent peak to RMS level • excellent signal to noise ratio • good for nonlinear characterization • leakage free measurements obtained

DISADVANTAGES • slowest of all test methods

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Comparison - Random/Hann, Burst Random, Chirp

RANDOM

BURST RANDOM

SINE CHIRP

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Random with Hanning Window vs Burst Random

When comparing the measurement with random and burst random, notice that the random excitation peaks are lower and appear to be more heavily damped when compared to the burst random. - also notice the coherence improvement at the resonant peaks.

RANDOM

BURST RANDOM

RANDOM

BURST RANDOM

Frequency Response Function Coherence

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Random with Hanning Window vs Burst Random

RANDOM

BURST RANDOM

RANDOM & HANNING BURST RANDOM

COH

FRF

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Random with Hanning Window vs Burst Random

RANDOM & HANNING BURST RANDOM

COH

FRF

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Random with Hanning Window vs Burst Random

117Hz 143Hz

RANDOM

BURST RANDOM

• Windows will always have an effect on the measured FRF even when the same window is applied to both input and output signals

• There will always be a distortion at the peak and the appearance of higher damping

• Windows always, always, always, ... distort data!!!

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Linearity Check with Sine Chirp Excitation

ONE FORCE UNIT

FIVE FORCE UNITS

TEN FORCE UNITS

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Shaped Spectrum

S H A P E D S P E C T R U M E X C I T A T I O N

Uncontrolled broadband excitation techniques are used for most modal testing performed today. However, the relatively flat excitation spectrum causes a wide variation in the response accelerometers. This may be a problem when tesing sensitive equipment. A shaped spectrum, that is contolled, provides an input level that complements the response of the system. This provides a better usage of the ADC since wide variations in level over the frequency range of interest are minimized.

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Shaped Spectrum

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Multiple Input Multiple OutputShaker Testing

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53 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Multiple Input Shaker Excitation

� Discuss several practical aspects of multiple input multiple output shaker testing

� Discuss some tools commonly used in MIMO testing

Objectives of this lecture:

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54 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Multiple Input Shaker Excitation

� Provide a more even distribution of energy

� Simultaneously excite all modes of interest

� Multiple columns of FRF matrix acquired

� More consistent data is collected

� Same test time as SISO case

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Excitation Considerations - MIMO

Multiple referenced FRFs are obtained from MIMO test

Ref#1 Ref#2 Ref#3

Energy is distributed better throughout the structure making better measurements possible

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56 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Multiple Input Multiple Output Shaker Testing

Measurements are developed in a similar fashion to the single input single output case but using a matrix formulation

[ ] [ ][ ]FFXF GHG =

[ ]⎥⎥⎥⎥

⎢⎢⎢⎢

⎡=

Ni,No2,No1,No

Ni,22221

Ni,11211

HHH

HHH

HHH

H

L

MMM

L

L

[ ] [ ][ ] 1FFXF GGH −=

where

No - number of outputsNi - number of inputs

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57 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

MIMO Testing - Principal Component Analysis

Check for independent shaker inputs. Perform aSVD on the input shaker matrix commonly calledPrincipal Component Analysis

[ ] [ ][ ][ ]TFF VSUG =The singular values of the SVD should producelarge singular values at all frequencies for allshaker excitations. This indicates that theshaker excitation are linearly independent andinversion is possible

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58 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Multiple and Partial Coherence

Two additional coherence functions are needed:

Multiple coherence defines how much of the output signal is linearly related to all of the measured input signals. It is very similar to the ordinary coherence of the single input case.

Partial coherence relates how much of the measured output signal is linearly related to one of the measured input signal with the effects of the other measured input signals removed. All of the partial coherences sum together to form the multiple coherence.

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59 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Principal Component Analysis

Check for shaker linear independence

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60 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

MIMO FRF and Multiple Coherence

Typical MIMO measurements acquired

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61 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

SISO vs MIMO FRF

SISO FRF MIMO FRF

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RANDOM WITH WINDOW BURST RANDOM

SINGLE INPUT SINGLE OUTPUT TESTING

RANDOM WITH WINDOW BURST RANDOM

MULTIPLE INPUT MULTIPLE OUTPUT TESTING

Blue Frame -SISO vs MIMO -Reciprocity Checks

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63 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Blue Frame -SISO vs MIMO -Reciprocity Checks

SISO - RANDOM - HANNING - REF #1 & #2 MIMO - RANDOM - HANNING - REF #1 & #2

SISO - BURST RANDOM - REF #1 & #2 MIMO - BURST RANDOM - REF #1 & #2

FRFs look reasonably similar

but take a closer look

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64 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Blue Frame -SISO vs MIMO -Reciprocity Checks

Notice the variance on the FRF measured and the peak shifting

SISO - RANDOM - HANNING - REF #1

SISO - RANDOM - HANNING - REF #2

SISO - RANDOM - HANNING - REF #1 & #2

S I S O

RANDOM

HANNING

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65 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

SISO - BURST RANDOM - REF #1

SISO - BURST RANDOM - REF #2

SISO - BURST RANDOM - REF #1 & #2

S I S O

BURST

RANDOM

Blue Frame -SISO vs MIMO -Reciprocity Checks

Burst random improves the data but the peaks of the FRFsdo not remain the same when single shaker testing is performed

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66 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

MIMO - RANDOM - HANNING - REF #1

MIMO - RANDOM - HANNING - REF #2

MIMO - RANDOM - HANNING - REF #1 & #2

M I M O

RANDOM

HANNING

Blue Frame -SISO vs MIMO -Reciprocity Checks

MIMO random improves the consistency but there are other differences that can be seen at the anti-resonance

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MIMO - BURST RANDOM - REF #1 & #2

MIMO - BURST RANDOM - REF #2

MIMO - BURST RANDOM - REF #1

M I M O

BURST

RANDOM

Blue Frame -SISO vs MIMO -Reciprocity Checks

MIMO burst random improves the data in all respects

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68 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Blue Frame -SISO vs MIMO -Reciprocity Checks

The peaks are definitely shifted relative to the SISO and MIMO data

But which is the actual mode ???

SISO/MIMO - BURST RANDOM - REF #1 & #2 SISO/MIMO - BURST RANDOM - REF #1 & #2

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Excitation Considerations - MIMO

Large or complicated structures require special attention

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Excitation Considerations - MIMO

Multiple shakers are needed in order to adequately shaker the structure with sufficient energy to be able to make good measurements for FRF estimation

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Excitation Considerations - MIMO

Flimsy Dryer Cabinet requires special attention when measuring frequency response functions for modal testing. Extremely lightweight structures are very difficult to test and obtain quality FRFs

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Excitation Considerations - MIMO

Measurements on the same structure can show tremendously different modal densities depending on the location of the measurement

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Things no one ever told me !!!

Shaker testing is very powerful but there are many issues that must be understood.

Some of these are identified on the next pages

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74 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Reciprocity

Even on simple structures, reciprocity can be a problem but not due to the structure

Here is an example of a stinger flexibility due to rotation effects – the upper portion of the structure has a rotational effect

0 500Hz-90

0

dB(m

/s2)

/N

FRF 6:-X / 2:+XFRF 2:-X / 6:+X

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75 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Reciprocity – SISO FRF Measurements

Using SISO, several measurements were made at different locations as shown

While only a few sample measurements are shown, there is an effect of the shaker location on the structure and the rotational stinger effect.

0 900Hz-100

20

dBg/N

FRF 1:-Z/3:-ZFRF 3:-Z/1:-Z

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76 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Stinger Alignment or Damaged Stinger

An incorrectly aligned stinger or a poorly fabricated stinger can ruin a test

Here are two examples of the effect on an FRF measurement due to these problems

300.00 700.00Hz-40.00

40.00

dB( g/lb

f)

Straight StingerBent StingerImpact

Stinger Alignment Effects

300 700Hz-40

40

dBg/lb

f

Straight StingerBent StingerImpact

1000.00 1200.00Hz-20.00

35.00

dB( (m

/s2)

/N)Straight StingerDamaged Stinger

Damaged Stinger Effect

1000 1200Hz-20

35

dB( (m

/s2)

/NStraight StingerPoorly FabricatedStinger

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77 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Stinger Length

The length of the stinger can also have an impact on the measured response.

Too short a stinger will have higher lateral stiffness and too long a stinger will have flexibility

50.00 900.00Hz-80.00

30.00

dB(g/lb

f)

1 inch3 inch5 inch7 inchImpact

Stinger Length Comparisons

450.00 650.00Hz

-25.00

25.00

dB(g/lb

f)

1 inch3 inch5 inch7 inchImpact

Stinger Length Comparisons

450.00 650.00Hz

-25.00

25.00

dB(g/lb

f)

1 inch3 inch5 inch7 inchImpact

Stinger Length Comparisons

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78 Dr. Peter AvitabileStructural Dynamics & Acoustic Systems LabShaker Excitation

Stinger Type

There are many different stinger types

There can be an effect due to these differences

0.00 900.00Hz

-90.00

30.00

dB(g/lb

f)

Thin Drill RodThick Drill RodPiano WireNylon Threaded RodSteel Threaded RodImpact

Stinger Type Comparison

0 900Hz-90

30

dBg/lb

f

Thin Drill RodThick Drill RodPiano WireNylon Threaded RodSteel Threaded RodImpact

450 625Hz-25

20

dBg/lb

f

Thin Drill RodThick Drill RodPiano WireNylon Threaded RodSteel Threaded RodImpact

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Shaker Excitation

IMAC 27 - Orlando, FL - 2009

Peter Avitabile Marco PeresUMASS Lowell The Modal Shop