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Identification of material properties using full field measurements on vibrating plates

Identification of material properties using full field measurements on vibrating plates. Mr Baoqiao GUO, Dr Alain GIRAUDEAU, Prof. Fabrice PIERRON LMPF research group École Nationale Supérieure d’Arts et Métiers (ENSAM) Châlons en Champagne - France. Introduction.

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Identification of material properties using full field measurements on vibrating plates

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  1. Identification of material properties using full field measurements on vibrating plates Mr Baoqiao GUO, Dr Alain GIRAUDEAU, Prof. Fabrice PIERRON LMPF research group École Nationale Supérieure d’Arts et Métiers (ENSAM) Châlons en Champagne - France

  2. Introduction • Thin plates point clamped • Sine driving movement • Inertial excitation • Full field measurements Presentation of the procedure • Data processing using Virtual Fields Method (V.F.M.)

  3. Theory Constitutivelaw Principle of Virtual Work u*, e*=e(u*) Virtual fields Thin plates e <=> k Measured Chosen Unknown Virtual Fields Method Thin plates Sine vibrating response

  4. Theory = d.coswt + w(x,y,t) Driving mouvement Plate deformation (bending) Two fields to measure Virtual fields: m*(x,y,t) = d.coswt + Re [ (wr*(x,y) +j.wi*(x,y)) . exp(jwt) ] Two fields to select Actual out of plane deflection: m(x,y,t) = d.coswt + Re [ (wr(x,y)+j.wi(x,y)) . exp(jwt) ]

  5. Theory V.W.E.F. = 0 Selected k*(x,y), w*(x,y) Measured(w(x,y), k(x,y)) (r,w(x,y),w*(x,y)) Two selected virtuals fields : VF1, VF2

  6. Experimental Slope fields Deflectometry In phase p/2 lag Q d da P M CCD O l Measurements Deflection fields Curvature fields d = 2l . da

  7. Experimental Grid Images At rest Deformed Slopes - x x x Phases - y y y Spatial phase shifting Image Processing

  8. Experimental Experimental set up

  9. Experimental Out of resonance 80 Hz Near resonance 100 Hz Slope fields Plate : PMMA 200 x 160 x 3 mm3

  10. Experimental Noise filtering: polynomial fitting Deflection field: integration Curvature fields: differentiation No data (hole) High gradients: uncertain measurements Remove data before fitting

  11. Experimental Avril S., Grédiac M., Pierron F.Sensitivity of the virtual fields method to noisy data, Computational Mechanics, vol. 34, n° 6, pp. 439-452, 2004. 3x3 5x5 Use of optimal special virtual fields Use of piecewise virtual fields Toussaint E., Grédiac M., Pierron F., The virtual fields method with piecewise virtual fields, International Journal of Mechanical Sciences, vol. 48, n° 3, pp. 256-264, 2006. Zero contribution from the clamping area !

  12. Results Choice: degree 10 8 6 4 2 0 10 16 8 12 14 18 Influence of the degree of the polynomial fitting(80 Hz) Polynomial degree

  13. Results E b Mean 4.90 GPa 1.08 10-4s C. Var. 2.3% 3% Reference values Coupons: PMMA beams h = 4mm, l = 10mm, L= 107-114mm Clamped-free conditions Free vibrations, first bending mode ~80 Hz

  14. Results Reference values Assumption: n constant = 0.3 (manufacturer datasheet) (???)

  15. Results 3 x 3 5 x 5 GPa 10-4GPa.s GPa 10-4GPa.s CV # 0.4 % CV # 4 % CV # 0.6 % CV # 23 % Influence of number of virtual elements (80 Hz) reference

  16. Results 80 Hz 100 Hz GPa 10-4GPa.s GPa Influence of the frequency reference 10-4GPa.s

  17. Results Out of resonance 80 Hz Near resonance 100 Hz Poor SNR: take pictures at other times Influence of the frequency

  18. Results 80 Hz 100 Hz Influence of the frequency • constant ??? Material model ??? reference

  19. Conclusion Novel procedure for damping measurements At or out-of resonance Based on full-field slope measurements Main assets Direct method (no updating) Insensitive to clamping dissipation Poisson’s damping Future work Explore wider range of frequencies Apply to anisotropic plates (composites) Conclusion

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