Vibrations and Acoustic 2017-2018 7. Experimental Modal Analysis

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Arnaud Deraemaeker (aderaema@ulb.ac.be)

7. Experimental Modal Analysis

Vibrations and acoustics

*Principle of EMA

*Measuring FRFs

*SDOF Identification

*MDOF Identification

Outline of the chapter

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Vibrations and Acoustic 2017-2018 7. Experimental Modal Analysis

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Principle of EMA

1. Measure FRFs

2. Estimate poles (natural frequencies)

3. Identify mode shapes

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Principle of EMA

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Measuring FRFs

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Measuring FRFs : summary

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Use of windows : summary

No window (synchronisation !)

Exponential window to reduceeffect of noise (output) + force window (input)

Hanning window to reduce leakage

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Measuring FRFs

Shaker excitation

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Measuring FRFs

Roving hammer excitation

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Measuring FRFs

Reciprocity

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Measuring FRFs in practice

SDOF identification

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The pole-residue model in the frequency domain

The frequency response function of a one dof system is :

The Pole-residue model in the frequency domain is :

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The impulse response function of a one DOF system is :

The Pole-residue model in the time domain is :

The pole-residue model in the time domain

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Estimating parameters : Peak-picking method

Natural frequency (ratio k/m)

Damping coefficient (b)

Mass (m)

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Estimating parameters : logarithmic decrement method

Natural frequency (ratio k/m)

Damping coefficient (b)

Mass (m)

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Estimating parameters : curve fitting

More equations than unknowns

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Estimating parameters : curve fitting

More equations than unknowns

Moore-Penrose pseudo-inverse : Least-squares solution

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MDOF identification

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The pole-residue model in the frequency domain

The FRF matrix of a MDOF system is :

The Pole-residue model in the frequency domain is :

Ri is a matrix

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The Pole-residue model in the time domain is :

The pole-residue model in the time domain

Inverse Fourier transform

Ri is a matrix

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Estimating the poles : peak picking method

Natural frequencies and modal damping

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Estimating the mode shapes : curve fitting in the frequency domain

For each single FRF :

l=input, k=output

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Estimating the mode shapes

Mode shapes

Keep l fixed, vary k

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Estimating natural frequencies and mode shapes : the complex exponential method

l=input, k=output

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Estimating natural frequencies and mode shapes : the complex exponential method

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Estimating natural frequencies and mode shapes : the complex exponential method

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Estimating natural frequencies and mode shapes : the complex exponential method

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Model order and stabilisation diagram

N ?

N

s:stable in both freqand damping

d: stable in damping

f: stable in frequency