1. Experimentele Modale Analyse
LES 2 – THEORETISCHE ASPECTEN
Patrick Guillaume
Tel.: 02/
EXPERIMENTELE MODALE ANALYSIS, LES 2

2. Frequency Response of MDOF System
EXPERIMENTELE MODALE ANALYSIS, LES 2

3. Poles of SDOF System Poles : Generalized eigenvalue problem
EXPERIMENTELE MODALE ANALYSIS, LES 2

4. The SDOF Modal-Parameter Model
Pole p
Re - Decay rate
Im - Modal frequency
Residue R
Strength of the mode
EXPERIMENTELE MODALE ANALYSIS, LES 2

5. Poles and Residues Amplitude of mode is not given by the residue alone
Hi-Fi turntable
Car
Same pole
Different residues
EXPERIMENTELE MODALE ANALYSIS, LES 2

6. Multiple Degree of Freedom (MDOF)
Dynamic stiffness matrix
Transfer function matrix
EXPERIMENTELE MODALE ANALYSIS, LES 2

7. FREQUENCY RESPONSE FUNCTION IMPULSE RESPONSE FUNCTION
Poles of MDOF System
Poles:
FREQUENCY RESPONSE FUNCTION
IMPULSE RESPONSE FUNCTION
EXPERIMENTELE MODALE ANALYSIS, LES 2

8. Eigenvalues and Eigenvectors
No Damping
EXPERIMENTELE MODALE ANALYSIS, LES 2

9. Weighted Orthogonality of Modal Vectors
Pre-multiply with
Transpose the equation
EXPERIMENTELE MODALE ANALYSIS, LES 2

10. Weighted Orthogonality of Modal Vectors
Substracting
From eq. 1:
(eq. 1)
EXPERIMENTELE MODALE ANALYSIS, LES 2

11. Modal Mass and Stiffness
No Damping
Modal mass and stiffness are not unique !
EXPERIMENTELE MODALE ANALYSIS, LES 2

12. Modal Coordinates
EXPERIMENTELE MODALE ANALYSIS, LES 2

13. Modal Model
EXPERIMENTELE MODALE ANALYSIS, LES 2

14. Modal Decomposition
IRF
FRF
EXPERIMENTELE MODALE ANALYSIS, LES 2

15. Scaling of the Mode Shapes
EXPERIMENTELE MODALE ANALYSIS, LES 2

16. Proportional Damping
Eigenvalues
EXPERIMENTELE MODALE ANALYSIS, LES 2

17. Proportional Damping Complex system poles and normal modal vectors
Modal mass, stiffness and damping
EXPERIMENTELE MODALE ANALYSIS, LES 2

18. General Viscous Damping
EXPERIMENTELE MODALE ANALYSIS, LES 2

19. General Viscous Damping
Eigenvalues and vectors
Complex system poles and complex modal vectors
Orthogonality
EXPERIMENTELE MODALE ANALYSIS, LES 2

20. General Viscous Damping
Poles:
FREQUENCY RESPONSE FUNCTION
IMPULSE RESPONSE FUNCTION
EXPERIMENTELE MODALE ANALYSIS, LES 2

21. General Viscous Damping
EXPERIMENTELE MODALE ANALYSIS, LES 2

22. Operational Deflection Shapes (ODS)
Resonant frequencies (peaks)
Mode shapes (ODS)
EXPERIMENTELE MODALE ANALYSIS, LES 2

23. Operational Deflection Shapes (ODS)
Uncoupled modes (SDOF)
EXPERIMENTELE MODALE ANALYSIS, LES 2

24. Operational Deflection Shapes (ODS)
Coupled modes + =
EXPERIMENTELE MODALE ANALYSIS, LES 2

25. Force Appropriation Method
Also called:
Normal Mode Testing
Phase Resonance Testing
Traditionally used for Ground Vibration Testing (GVT) of airplanes (large structures)
First method to use multiple inputs
Find (mono-phased) forced vector to obtain a (mono-phased) response vector with a 90 degree phase
EXPERIMENTELE MODALE ANALYSIS, LES 2

26. Force Appropriation Method
Real/imaginary part
Find (mono-phased) forced vector to obtain a (mono-phased) response vector with a 90 degree phase
Verification of normal mode tuning by turning off the excitations
EXPERIMENTELE MODALE ANALYSIS, LES 2

27. MatLab Oefening modal_model.m SDOF MDOF Eigenwaarden en vectoren
Schaling van de eigenvectoren
EXPERIMENTELE MODALE ANALYSIS, LES 2