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A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne

CompTest. 2003. Identification of stiffness and damping properties of composites from full field measurements Theory and simulations. A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne. Scheme. 1. Introduction. 2. Presentation of the method. 3. Virtual Fields.

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A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne

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  1. CompTest 2003 Identification of stiffness and damping properties of composites from full field measurementsTheory and simulations A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne

  2. Scheme 1. Introduction 2. Presentation of the method 3. Virtual Fields 4. Application 5. Simulation & Validation 6. Conclusion A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  3. Introduction - Stiffness Material properties Modal properties Number of parameters Vibrating plates Heterogenous tests Prediction of vibrating behaviour - Damping Identification : Experimental Modal Analysis Anisotropic materials Isotropic material Anisotropic material A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  4. Presentation of the method • Extension of the Virtual Fields Method (Grédiac 1989) • 3 Points : • Excitation set up • Full field measurements • Application of the Principle of Virtual Works A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  5. Excitation set up Plate clamped in one point Sine driven movement Out of plane vibrations Inertial excitation In vacuum In air A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  6. Full field measurements Optical methods : Aluminium plate +1.5 mm -1.5 In air In vacuum - fields of out of plane slopes - no contact Examples : Speckle Interferometry measurements A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  7. Principle of Virtual Works Inertial forces Internal forces External forces u* : virtual displacement Virtual Fields e* : virtual strain tensor Choice of the Virtuals Fields Virtual works : (Elastic) (Dissipative) (Clamping) (Acceleration) A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  8. Actual fields of displacements y x O z Phase Amplitude Mode k • Harmonic driven movement : • Absolute response : A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  9. F. E. Simulation Rectangular plate Responses Mode In phase p/2 lag - 0 Freq.1 26.9 Hz -40 mm -80 Imaginary Real +100 Freq.3 150 Hz - 0 mm -150 Isotropicand viscoelastic material Model : 2048 shell elements A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  10. Actual fields of displacements y x O z • Harmonic driven movement : • Absolute response : • Absolute response in complex notation : A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  11. Choice of the Virtuals Fields Complex Virtual Fields • Kinematically admissible : Actual fields : Virtual fields : A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  12. Virtual works of external forces (VWEF) VWEF F Clamping : u* VWEF A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  13. Virtual works of internal forces (VWIF) + - • Thin plate : Love Kirchoff theory • Isotropic viscoelastic material A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  14. Virtual works of inertial forces (VWIF) Acceleration : A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  15. Summary Eq1 (no time dep.) Eq2 (cos(2wt)) 3 equations Eq3 (sin(2wt)) * * • for any combination of u and u i r 4 independants equations 6 equations : VWIF + VWEF = VWAC Virtual Works Principle : • at any time A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  16. Identification Measured with : Choosen Unknown • Objective function : • Interest for 2 equations : A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  17. Simulation Rectangular plate F E model : Virtual fields : Identification Isotropic material Proportional damping : b 2048 shell elements A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  18. Simulation – Results (1) -5 b =10 Proportional damping : Dxx b Dxy 5 Relative errors (%) 0 Noise level (%p-p) -5 27 Hz 71 Hz 150 Hz 171 Hz Frequencies Excitation at resonances A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  19. Simulation – Results (2) Dxy -3 b =10 Proportional damping : Dxx b Dxy 5 Relative errors (%) 0 Noise level (%p-p) -5 27 Hz 71 Hz 150 Hz 171 Hz Frequencies Excitation at resonances A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  20. Simulation – Results (3) -3 b =10 Proportional damping : Dxx Dxy b Dxy Excitation at NON resonance 5 Relative errors (%) 0 Noise level (%p-p) -5 50 Hz 100 Hz 150 Hz 200 Hz Frequencies A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

  21. Conclusion Anisotropic plates Identification of frequency dependance of damping • Simultaneous identification of stiffness and damping • Material damping • Plate of any shape • Resonant or non resonant response • Set of specimens • Excitation on a range of frequencies A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003

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