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Identification of stiffness and damping properties of composites from full field measurements Theory and simulations A. Giraudeau, F. Pierron L.M.P.F.

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Presentation on theme: "Identification of stiffness and damping properties of composites from full field measurements Theory and simulations A. Giraudeau, F. Pierron L.M.P.F."— Presentation transcript:

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 Châlons / 01 / Scheme 1. Introduction 2. Presentation of the method 3. Virtual Fields 4. Application 5. Simulation & Validation 6. Conclusion

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

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

9 A. Giraudeau, F. Pierron - CompTest Châlons / 01 / F. E. Simulation Model : Isotropic and viscoelastic material mm Rectangular plate 2048 shell elements Freq Hz Mode Freq Hz mm -80 In phase  /2 lag Responses Real Imaginary

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

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

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

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

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

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

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

18 A. Giraudeau, F. Pierron - CompTest Châlons / 01 / 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 (%) Dxx Dxy 

19 A. Giraudeau, F. Pierron - CompTest Châlons / 01 / 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 (%) Dxx Dxy 

20 A. Giraudeau, F. Pierron - CompTest Châlons / 01 / 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 (%) DxxDxy 

21 A. Giraudeau, F. Pierron - CompTest Châlons / 01 / 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


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