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Identification of local material damping in vibrating plates using full-field measurements

7 th International Conference on Modern Practice in Stress and Vibration Analysis, 8-10 th September 2009, Cambridge. Identification of local material damping in vibrating plates using full-field measurements. Alain Giraudeau, Fabrice PIERRON LMPF research group Arts et Métiers ParisTech

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Identification of local material damping in vibrating plates using full-field measurements

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

  2. 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 testN.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, 2002. • 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 A. Giraudeau, F. Pierron - 2009 MPSVA conference

  3. F(t) Unknown energy loss Attachements : Parasistic effects Equilibrium of forces No energy consideration Principle Stiffness Damping Identification of material properties : • Thin plate specimens • Dynamic loading A. Giraudeau, F. Pierron - 2009 MPSVA conference

  4. M ui* ui* ui* Principle of Virtual Work (P V W) Principle F(t) Dynamic equilibrium : • Point M : • Continuous • Differentiable • Observed area Internal f. Inertial f. Boundary f. Volumic f. A. Giraudeau, F. Pierron - 2009 MPSVA conference

  5. Considered case Principle • Rectangular thin plate • Clamped on small area • Sine driving movement • Inertial excitation • Full field measurements • Data processing using Virtual Fields Method (V.F.M.) A. Giraudeau, F. Pierron - 2009 MPSVA conference

  6. Constitutive law Thin plates e <=> k Measured Selected Unknown Virtual Fields Method Principle of Virtual Work u* e*=e(u*) Sine vibrating response Thin plates A. Giraudeau, F. Pierron - 2009 MPSVA conference

  7. G Virtual Fields Method = 0 = 0 V. F. Selection : along G A. Giraudeau, F. Pierron - 2009 MPSVA conference

  8. Virtual Fields Method P V W Selected k*(x,y), w*(x,y) Measured(w(x,y), k(x,y)) (w(x,y),w*(x,y)) Two selected virtuals fields : VF1, VF2 Direct resolution of an inverse problem A. Giraudeau, F. Pierron - 2009 MPSVA conference

  9. Slope fields Deflectometry In phase p/2 lag Q d da P M CCD O l Experimental arrangement Deflection fields Curvature fields d = 2l . da A. Giraudeau, F. Pierron - 2009 MPSVA conference

  10. Grid Images At rest Deformed Slopes - x x x Phases - y y y Experimental arrangement Image Processing Spatial phase evaluation A. Giraudeau, F. Pierron - 2009 MPSVA conference

  11. Experimental arrangement Experimental set-up A. Giraudeau, F. Pierron - 2009 MPSVA conference

  12. Slope / X Slope / Y Deflection Real Imaginary 0.41 mrad / col. 0.17 mrad / col. m 34 m / col. Results Images (examples) 80Hz (out of resonance) A. Giraudeau, F. Pierron - 2009 MPSVA conference

  13. w*(x,y) = 0 *(x,y) = 0 Results Virtual fields selection Piecewise virtual fields (Toussaint et al., IJMS, 2006) G A. Giraudeau, F. Pierron - 2009 MPSVA conference

  14. 0.056 DMTA Results Reference values Coupons: polycarbonate beams h = 4mm, l = 10mm, L= 107-114mm Clamped-free conditions Free vibrations, first bending mode A. Giraudeau, F. Pierron - 2009 MPSVA conference

  15. (Beams, DMTA) 80 Hz 100 Hz reference (non res.) (res.) GPa Poisson rat. loss factor Results A. Giraudeau, F. Pierron - 2009 MPSVA conference

  16. Driving mvt. 100 Hz 2nd accel. Results Boundary condition effects 2nd accelerometer Rubber washers • = 34° tan(f)=0.67 A. Giraudeau, F. Pierron - 2009 MPSVA conference

  17. Initial clamping With rubber washers Poisson rat. loss factor Results Boundary condition effects (2) 100 Hz GPa tan(f)=0.67 A. Giraudeau, F. Pierron - 2009 MPSVA conference

  18. G w*(x,y) = 0 *(x,y) = 0 Results Additional damping effect Viscoelastic patch at back surface A. Giraudeau, F. Pierron - 2009 MPSVA conference

  19. Initial clamping With rubber washers Poisson rat. loss factor Results Additional damping effect (2) 100 Hz GPa A. Giraudeau, F. Pierron - 2009 MPSVA conference

  20. 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 A. Giraudeau, F. Pierron - 2009 MPSVA conference

  21. Local damping Conclusion Soundboard of a guitar A. Giraudeau, F. Pierron - 2009 MPSVA conference

  22. 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 A. Giraudeau, F. Pierron - 2009 MPSVA conference

  23. Thank you for your attention Sponsored by the Champagne-Ardenne Regional Council www.lmpf.net A. Giraudeau, F. Pierron - 2009 MPSVA conference

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