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Experimentele Modale Analyse

Experimentele Modale Analyse. LES 2 – THEORETISCHE ASPECTEN. Patrick Guillaume E-mail: patrick.guillaume@vub.ac.be Tel.: 02/6293566. Frequency Response of MDOF System. Poles of SDOF System. Poles : Generalized eigenvalue problem. The SDOF Modal-Parameter Model. Pole p

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Experimentele Modale Analyse

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  1. Experimentele Modale Analyse LES 2 – THEORETISCHE ASPECTEN Patrick Guillaume E-mail: patrick.guillaume@vub.ac.be Tel.: 02/6293566 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. Poles of MDOF System • Poles: IMPULSE RESPONSE FUNCTION FREQUENCY 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: IMPULSE RESPONSE FUNCTION FREQUENCY 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

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