1 Characteristics and Presentation of MDOF FRF Data Modal Analysis and Modal Testing S. Ziaei Rad.
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Transcript of 1 Characteristics and Presentation of MDOF FRF Data Modal Analysis and Modal Testing S. Ziaei Rad.
1
Characteristics and Presentation of MDOF FRF Data
Modal Analysis and Modal Testing
S. Ziaei Rad
2
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
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Receptance and Impedance FRF Parameters
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
Receptance and Impedance FRF Parameters
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.
5
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)
7
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
18
19
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.