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:
A general element of the receptance is given by:

3. Receptance and Impedance FRF Parameters
Now, let’s look at the Impedance matrix [Z]:
Therefore, we can not simply write:
Looking at the definition of a typical element of [Z]:

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)

6. FRF Plot in MDOF System Typical mobility FRF plot for MDOF system
(individual modal contribution)

7. Point and Transfer FRFs
Point FRF

8. 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.

9. Ponit and transfer FRF for 6DOF systemk1 k2 k3 k6 k4 k5 m1 m2 m3 m4 m5 m6 x1 x2 x3 x4 x5 x6
m1=m2=m3=m4=m5=m6=1 Kg
k1=k2=k3=k4=k5=k6= N/m

10. FRFs of 6DOF System
H11
H21
H31
H41
H51
H61

11. Display of FRF Data For Damped Systems
Bode Plots
Nyquist diagrams
Real and Imaginary plots
Three-dimensional plots

12. 2DOF System k1 k2 m1 m2 x1 x2 m1=m2=1 Kg k1=k2=360 kN/M
Hysteretic damping

13. Bode Plot
H12
H11

14. Nyquist Plot
H12
H11

15. Real and Imaginary
H11
H12

16. 3D Plot

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.