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
A general element of the receptance is given by
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Receptance and Impedance FRF Parameters
Now, lets look at the Impedance matrix Z
Therefore, we can not simply write
Looking at the definition of a typical element of
Z
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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.

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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
Transfer FRF
Point 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
k1
k3
k6
k2
k4
k5
m5
m4
m3
m2
m6
m1
x1
x2
x3
x4
x5
x6
m1m2m3m4m5m61 Kg k1k2k3k4k5k6100000
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
k2
k1
m2
m1
x1
x2
m1m21 Kg k1k2360 kN/M
Hysteretic damping
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Bode Plot
H12
H11
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Nyquist Plot
H12
H11
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Real and Imaginary
H11
H12
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3D Plot
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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.