Characteristics and Presentation of MDOF FRF Data

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Characteristics and Presentation of MDOF FRF Data

Modal Analysis and Modal Testing

S. Ziaei Rad

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Receptance and Impedance FRF Parameters

The Relation between different form of FRF can be stated as before:

)]([)]([

)]([)]([

)]([)]([

2

HA

YiA

HiY

A general element of the receptance is given by:

) (,,1 0 , )( klNlFF

XH l

k

jjk

3


Now, let’s look at the Impedance matrix [Z]:

}{][}]{[}{

}]{[}{1 FHFZF

FHX

Therefore, we can not simply write:

1

)(jk

jk ZH

Looking at the definition of a typical element of [Z]:

) (,,1 0 , )( klNlXX

FZ l

k

jjk

4


To measure the receptance, we should make sure that just a single excitation force is applying on the structure.

To measure an impedance property all DOFs except one should be grounded.

Such a condition is almost impossible to achieve in practical situation.

Therefore, only types of FRF which can expect to measure directly are those of the mobility or receptance type.

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Some Definitions

A Point Mobility (or receptance) is one where the response DOF and the excitation coordinate are identical.

A Transfer Mobility is one where the response and excitation DOFs are different.

A Direct Mobility is one where types of DOFs for response and excitation are identical. (both in x)

A Cross Mobility is one where types of DOFs for response and excitation are not identical. (one in x and other in y direction)

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FRF Plot in MDOF System

Typical mobility FRF plot for MDOF system (individual modal contribution)

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Point and Transfer FRFs

Point FRF Transfer FRF

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Point and Transfer FRFs

There is an anti-resonance after each resonance in point FRF.

In point FRF the modal constant for every mode is positive, it being the square of a number.

In transfer FRF, there is an anti-resonance or a minima after each resonance.

We expect a transfer FRF between two positions widely separated on the structure to exhibit fewer anti-resonances than one for two points relatively close together. (the further apart are the two points, the more likely are the two eigen vectors elements to alternate in sign as one progress through the modes.

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Ponit and transfer FRF for 6DOF system

m5m4m3m2 m6m1

x1 x2 x3 x4 x5 x6

k1 k2 k3 k4 k5 k6

m1=m2=m3=m4=m5=m6=1 Kgk1=k2=k3=k4=k5=k6=100000 N/m

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FRFs of 6DOF System

H11 H21 H31

H41 H51 H61

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Display of FRF Data For Damped Systems

Bode Plots Nyquist diagrams Real and Imaginary plots Three-dimensional plots

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2DOF System

m2m1

x1 x2

k1 k2

m1=m2=1 Kgk1=k2=360 kN/M 04.0

02.0

2

1

Hysteretic damping

222)(

rr

krjrjk i

H

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Bode Plot

H11 H12

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Nyquist Plot

H11 H12

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Real and Imaginary

H11 H12

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3D Plot

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1

1

2

r

rj

C j r

j r

r

r

exp

1

2

C j r

j r

Dr

r

r

exp

1

2

C j r

j r

r

r

r

exp

1

2

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Conclusions

The purpose of this session has been to predict the form which will be taken by plots of FRF data using the different display format.

Although the graphs were taken from some theoretical models, they can help to understand and interpret actual measured data.

Characteristics and Presentation of MDOF FRF Data

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