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

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

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

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

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

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

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

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

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

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 :

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

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

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

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

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

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

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

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 

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 

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 

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