1/23 A. Giraudeau, F. Pierron MPSVA conference Identification of local material damping in vibrating plates using full-field measurements Alain Giraudeau, Fabrice PIERRON LMPF research group Arts et Métiers ParisTech Châlons en Champagne - France 7 th International Conference on Modern Practice in Stress and Vibration Analysis, 8-10 th September 2009, Cambridge

2/23 A. Giraudeau, F. Pierron MPSVA conference Motivation / Objectives  Material damping  Difficult to measure  Problem with connections/joints  Most of the standard techniques rely on beams  Difficult (but important) to get both complex stiffnesses on same test N.W. Tschoegl, W.G. Knauss, and I. Emri. Poisson's ratio in linear viscoelasticity - a critical review. Mechanics of Time-Dependent Materials, 6:3-51,  Objectives  Simultaneous identification of both complex stiffnesses (isotropy) on single test  Method to cancel the effect of connections  Explore the use of full-field measurements

3/23 A. Giraudeau, F. Pierron MPSVA conference Identification of material properties : Stiffness Damping  Thin plate specimens  Dynamic loading Attachements :Parasistic effects Unknown energy loss Equilibrium of forces No energy consideration F(t) Principle

4/23 A. Giraudeau, F. Pierron MPSVA conference Dynamic equilibrium :  Point M :  Observed area Internal f. Boundary f.Volumic f. Inertial f. Principle of Virtual Work (P V W) - Continuous - Differentiable ui*ui* ui*ui*ui*ui* Principle F(t) M

5/23 A. Giraudeau, F. Pierron MPSVA conference Considered case  Rectangular thin plate  Sine driving movement  Inertial excitation  Full field measurements  Data processing using Virtual Fields Method (V.F.M.)  Clamped on small area Principle

6/23 A. Giraudeau, F. Pierron MPSVA conference Principle of Virtual Work u*u* Thin plates Sine vibrating response  *=  ( u *) Constitutive law Unknown Thin plates  k SelectedMeasured Virtual Fields Method

7/23 A. Giraudeau, F. Pierron MPSVA conference along  V. F. Selection : = 0  Virtual Fields Method

8/23 A. Giraudeau, F. Pierron MPSVA conference P V W Measured ( w(x,y), k(x,y)) Selected k*(x,y), w*(x,y) (w(x,y),w*(x,y)) Two selected virtuals fields : VF1, VF2 Direct resolution of an inverse problem Virtual Fields Method

9/23 A. Giraudeau, F. Pierron MPSVA conference Deflectometry CCD O M P Q Deflection fields Curvature fields Slope fields In phase  /2 lag  dd . d  Experimental arrangement

10/23 A. Giraudeau, F. Pierron MPSVA conference Image Processing Grid Images At restDeformed Phases xx y y - Slopes x - y Spatial phase evaluation Experimental arrangement

11/23 A. Giraudeau, F. Pierron MPSVA conference Experimental set-up Experimental arrangement

12/23 A. Giraudeau, F. Pierron MPSVA conference Deflection 34  m / col. 80Hz (out of resonance) Images (examples) Results

13/23 A. Giraudeau, F. Pierron MPSVA conference Piecewise virtual fields (Toussaint et al., IJMS, 2006) w*(x,y) = 0  *(x,y) = 0  Virtual fields selection Results

14/23 A. Giraudeau, F. Pierron MPSVA conference Reference values Coupons: polycarbonate beams h = 4mm, l = 10mm, L= mm Clamped-free conditions Free vibrations, first bending mode E (GPa)  ( = tan(  ) ) Means C. variation 2.4%5.2% DMTA Results

15/23 A. Giraudeau, F. Pierron MPSVA conference Results 80 Hz 100 Hz reference (Beams, DMTA) (non res.) (res.) Poisson rat. loss factor GPa

16/23 A. Giraudeau, F. Pierron MPSVA conference Boundary condition effects Rubber washers 2 nd accelerometer  = 34° tan(  )= nd accel. Driving mvt. 100 Hz Results

17/23 A. Giraudeau, F. Pierron MPSVA conference GPa Poisson rat. loss factor Initial clampingWith rubber washers Boundary condition effects (2) 100 Hz tan(  )=0.67 Results

18/23 A. Giraudeau, F. Pierron MPSVA conference Additional damping effect Viscoelastic patch at back surface  w*(x,y) = 0  *(x,y) = 0 Results

19/23 A. Giraudeau, F. Pierron MPSVA conference GPa Poisson rat. loss factor Initial clampingWith rubber washers Additional damping effect (2) 100 Hz Results

20/23 A. Giraudeau, F. Pierron MPSVA conference Conclusion  Simultaneous identification of stiffness and damping  Material damping  Resonant or non resonant response  Information on localization phenomena  Low sensitivity to boundary conditions  Could be applied to in-plane vibrations  Plate of any shape  Part of a component

21/23 A. Giraudeau, F. Pierron MPSVA conference Conclusion Soundboard of a guitar Local damping

22/23 A. Giraudeau, F. Pierron MPSVA conference Conclusion  Improvements  Time synchronization: high speed camera  Better fixture (sweep over large frequency range)  Future work  Apply to composite plates (anisotropy)  Test on more complex structures

23/23 A. Giraudeau, F. Pierron MPSVA conference Thank you for your attention Sponsored by the Champagne-Ardenne Regional Council