1. Experimentele Modale Analyse
LES 1 – THEORETISCHE INLEIDING
Patrick Guillaume
Tel.: 02/
4/6/2019
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

2. Overzicht cursus Theoretische basisbegrippen Meettechnieken
Niet-parametrische schattingen
Parametrische schattingen
Toepassingen
Gevoeligheidsanalyse
FE Model “updating”
“Substructuring”
“Operationele” modale analyse
“Structural Health Monitoring”
“Flight Flutter Testing”
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

3. EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

4. EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

5. EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

6. Frequency Response of MDOF System
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

7. Basic Equations of Motion for SDOF System
Time domain
Frequency domain (Laplace)
Dynamic Stiffness Z(s)  (static) stiffness k
Transfer function
Frequency response function (FRF)
x(t)
f(t)
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

8. Poles of SDOF System Poles : Generalized eigenvalue problem
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

9. The SDOF Modal-Parameter Model
Pole p
Re - Decay rate
Im - Modal frequency
Residue R
Strength of the mode
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

10. 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 1, 2005

11. Basic Equations for a 2-DOF System
Forces acting on mass 1
Sum forces = 0
x1(t)
x2(t)
f1(t)
f2(t) m2 k1 c1 m1 c2 k2
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

12. Basic Equations for a 2-DOF System
Time domain
Frequency domain (Laplace)
Matrix notations
Dynamic stiffness matrix
Transfer function matrix
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

13. FRF of 2-DOF System f2(t) m2 x2(t) f1(t) k2 c2 m1 x1(t) k1 c1 0° -180°
-360°
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

14. Multiple Degree of Freedom (MDOF)
Dynamic stiffness matrix
Transfer function matrix
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

15. FREQUENCY RESPONSE FUNCTION IMPULSE RESPONSE FUNCTION
Poles of MDOF System
Poles:
FREQUENCY RESPONSE FUNCTION
IMPULSE RESPONSE FUNCTION
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

16. Eigenvalues and Eigenvectors
No Damping
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

17. Weighted Orthogonality of Modal Vectors
Pre-multiply with
Transpose the equation
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

18. Weighted Orthogonality of Modal Vectors
Substracting
From eq. 1:
(eq. 1)
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

19. Modal Mass and Stiffness
No Damping
Modal mass and stiffness are not unique !
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

20. Modal Coordinates
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

21. Modal Model
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

22. Modal Decomposition
IRF
FRF
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

23. Scaling of the Mode Shapes
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

24. Proportional Damping Eigenvalues
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

25. Proportional Damping Complex system poles and normal modal vectors
Modal mass, stiffness and damping
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

26. General Viscous Damping
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

27. General Viscous Damping
Eigenvalues and vectors
Complex system poles and complex modal vectors
Orthogonality
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

28. General Viscous Damping
Poles:
FREQUENCY RESPONSE FUNCTION
IMPULSE RESPONSE FUNCTION
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

29. General Viscous Damping
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

30. Operational Deflection Shapes (ODS)
Resonant frequencies (peaks)
Mode shapes (ODS)
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

31. Operational Deflection Shapes (ODS)
Uncoupled modes (SDOF)
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

32. Operational Deflection Shapes (ODS)
Coupled modes + =
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

33. 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 1, 2005

34. 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 1, 2005

35. MatLab Oefening modal_model.m SDOF MDOF Eigenwaarden en vectoren
Schaling van de eigenvectoren
EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005