1. 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 CompTest 2003

2. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20032 Scheme 1. Introduction 2. Presentation of the method 3. Virtual Fields 4. Application 5. Simulation & Validation 6. Conclusion

3. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20033 Introduction Prediction of vibrating behaviour Material properties - Stiffness - Damping Identification : Experimental Modal Analysis Modal properties Anisotropic materials Heterogenous tests Number of parameters Anisotropic material Isotropic material Vibrating plates

4. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20034 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

5. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20035 In air Excitation set up Plate clamped in one pointSine driven movement Inertial excitation In vacuum Out of plane vibrations

6. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20036 Full field measurements Optical methods : - no contact - fields of out of plane slopes -1.5 +1.5 mm In airIn vacuum Aluminium plate Examples : Speckle Interferometry measurements

7. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20037 Principle of Virtual Works Virtual works : Internal forces External forces Inertial forces Choice of the Virtuals Fields (Elastic) (Dissipative) (Clamping)(Acceleration) u* : virtual displacement  * : virtual strain tensor Virtual Fields

8. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20038 Actual fields of displacements x yO z  Harmonic driven movement :  Absolute response : Amplitude Phase Mode k

9. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 20039 F. E. Simulation Model : Isotropic and viscoelastic material mm -150 +100 - 0 Rectangular plate 2048 shell elements Freq.1 26.9 Hz Mode Freq.3 150 Hz - 0 -40 mm -80 In phase  /2 lag Responses Real Imaginary

10. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200310 Actual fields of displacements x y O z  Harmonic driven movement :  Absolute response :  Absolute response in complex notation :

11. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200311 Choice of the Virtuals Fields  Kinematically admissible : Actual fields : Virtual fields : Complex Virtual Fields

12. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200312 Virtual works of external forces (VWEF) VWEF Clamping : F u* VWEF

13. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200313 Virtual works of internal forces (VWIF)  Thin plate : Love Kirchoff theory  Isotropic viscoelastic material + -

14. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200314 Virtual works of inertial forces (VWIF) Acceleration :

15. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200315 Summary Virtual Works Principle : VWIF + VWEF = VWAC  at any time 3 equations Eq1 (no time dep.) Eq2 (cos(2  t)) Eq3 (sin(2  t))  for any combination of u and u r * i * 6 equations : 4 independants equations

16. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200316 Identification  Interest for 2 equations : with : Measured Choosen  Objective function : Unknown

17. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200317 Simulation Isotropic material F E model : Rectangular plate 2048 shell elements Proportional damping :  Virtual fields : Identification

18. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200318 Excitation at resonances Simulation – Results (1) Proportional damping : -5  =10 Noise level (%p-p) 27 Hz 71 Hz 150 Hz 171 Hz Frequencies Relative errors (%) 0 5 -5 Dxx Dxy 

19. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200319 Excitation at resonances Simulation – Results (2) Proportional damping : -3  =10 Noise level (%p-p) 27 Hz 71 Hz 150 Hz 171 Hz Frequencies Relative errors (%) 0 5 -5 Dxx Dxy 

20. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200320 Simulation – Results (3) Proportional damping : -3  =10 Excitation at NON resonance Noise level (%p-p) 50 Hz 100 Hz 150 Hz 200 Hz Frequencies Relative errors (%) 0 5 -5 DxxDxy 

21. A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 200321 Conclusion  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 Identification of frequency dependance of damping Anisotropic plates