Experimental Mechanics

, Volume 46, Issue 6, pp 777–787 | Cite as

Stiffness and Damping Identification from Full Field Measurements on Vibrating Plates

  • A. Giraudeau
  • B. Guo
  • F. Pierron


The paper presents an experimental application of a method leading to the identification of the elastic and damping material properties of isotropic vibrating plates. The theory assumes that the searched parameters can be extracted from curvature and deflection fields measured on the whole surface of the plate at two particular instants of the vibrating motion. The experimental application consists in an original excitation fixture, a particular adaptation of an optical full-field measurement technique, a data preprocessing giving the curvature and deflection fields and finally in the identification process using the Virtual Fields Method (VFM). The principle of the deflectometry technique used for the measurements is presented. First results of identification on an acrylic plate are presented and compared to reference values. Results are discussed and improvements of the method are proposed.


Identification Virtual fields method Damping Forced vibrations Optical measurements Grid method Deflectometry Slope fields 


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  1. 1.
    Araujo AL, Mota Soares CM, Freitas MJM (1996) Characterization of material parameters of composite specimens using optimization and experimental data. Compos Part B 27(2):185–191.CrossRefGoogle Scholar
  2. 2.
    Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34(6):439–452.CrossRefzbMATHGoogle Scholar
  3. 3.
    Bishop JE, Kinra VK (1992) Some improvements in the flexural damping measurement techniques. In: Mechanics and mechanisms of material damping, pp 457–470.Google Scholar
  4. 4.
    Cugnoni J, Gmür T, Schorderet A (2004) Identification by modal analysis of composite structures modelled with FSDT and HSDT laminated shell finite elements. Compos Part A 35(7–8):977–987.CrossRefGoogle Scholar
  5. 5.
    Fällström KE, Olofsson K, Saldner HO, Schedin S (1996) Dynamic material parameters in an isotropic plate estimated by phase-stepped holographic interferometry. Opt Lasers Eng 24(5–6):429–454.CrossRefGoogle Scholar
  6. 6.
    Finegan IC, Gibson RF (1999) Recent research on enhancement of damping in polymer composite. Compos Struct 44:89–98.CrossRefGoogle Scholar
  7. 7.
    Frederiksen PS (1997) Experimental procedure and results for the identification of elastic constants of thick orthotropic plates. J Compos Mater 31(4):360–382.Google Scholar
  8. 8.
    Frederiksen PS (1997) Numerical studies for identification of orthotropic elastic constants of thick plates. Eur J Mech A, Solids 16:117–140.zbMATHGoogle Scholar
  9. 9.
    Gibson RF, Plunkett R (1976) Dynamic behavior of fiber-reinforced composites: measurements and analysis. J Compos Mater 10:325–332.Google Scholar
  10. 10.
    Gibson RF (1992) Damping characteristics of composites materials and structures. J Mater Eng Perform 1:11–20.Google Scholar
  11. 11.
    Gibson RF (2000) Modal vibration response measurements for characterization of composite materials and structures. Compos Sci Technol 60:2769–2780.CrossRefGoogle Scholar
  12. 12.
    Giraudeau A, Pierron F, Chambard J-P (2002) Experimental study of air effect on vibrating lightweight structures. In: SEM Annual Congress on Experimental Mechanics. Society for Experimental Mechanics. 10–12 June in Milwaukee, USA.Google Scholar
  13. 13.
    Giraudeau A, Pierron F (2005) Identification of stiffness and damping properties of thin isotropic plates using the virtual fields method. Theory and simulations. J Sound Vib 284(3–5):757–781.CrossRefGoogle Scholar
  14. 14.
    Grédiac M, Fournier N, Paris P-A, Surrel Y (1998) Direct determination of elastic constants of anisotropic plates by modal analysis: experimental results. J Sound Vib 210(5):643–659.CrossRefGoogle Scholar
  15. 15.
    Grédiac M, Paris P-A (1996) Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects. J Sound Vib 193(3):401–415.CrossRefGoogle Scholar
  16. 16.
    Grédiac M, Toussaint E, Pierron F (2000) Special virtual fields for the direct determination of material parameters with the virtual fields method. 1—principle and definition. Int J Solids Struct 39(10):2691–2705.CrossRefGoogle Scholar
  17. 17.
    Jiejun V, Chenggong L, Dianbin W, Manchang G (2003) Damping and sound absorption properties of particle Al matrix composite foams. Compos Sci Technol 63:569–574.CrossRefGoogle Scholar
  18. 18.
    McIntyre ME, Woodhouse J (1988) On measuring the elastic and damping constants of orthotropic sheet materials. Acta Metall 36(6):1397–1416.CrossRefGoogle Scholar
  19. 19.
    Ouis D (2003) Effect of structural defects on the strength and damping properties of a solid material. Eur J Mech A, Solids 22:47–54.CrossRefzbMATHGoogle Scholar
  20. 20.
    Srikanth N, Gupta M (2003) Damping characterization of magnesium based composites using an innovative circle-fit approach. Compos Sci Technol 63:559–568.CrossRefGoogle Scholar
  21. 21.
    Surrel Y, Fournier N, Grédiac M, Paris P-A (1998) Phase-stepped deflectometry applied to shape measurement of bent plates. Exp Mech 39(1):66–70.CrossRefGoogle Scholar
  22. 22.
    Surrel Y (2000) Customized phase shift algorithms. In: Rastogi P, Inaudi D (eds) Trends in optical non-destructive testing and inspection. Elsevier Science, pp 71–83.Google Scholar
  23. 23.
    Surrel Y (2003) Optique C1.
  24. 24.
    Surrel Y (2004) Deflectometry: a simple and efficient non interoferometric method for slope measurement. In: SEM Annual Congress on Experimental Mechanics. Society for Experimental Mechanics, in Costa Mesa, California, USA, pp 7–10, June.Google Scholar
  25. 25.
    Talbot JP, Woodhouse J (1997) The vibration damping of laminated plates. Compos Part A 28:1007–1012.CrossRefGoogle Scholar
  26. 26.
    Toussaint E, Grédiac M, Pierron F (2006) The virtual fields method with piecewise virtual fields. Int J Mech Sci 48(3):256–264.CrossRefGoogle Scholar
  27. 27.
    Wren GG, Kinra VK (1992) Modeling and measurement of axial and flexural damping in metal–matrix composites. In: Mechanics and mechanisms of material damping, pp 282–315.Google Scholar
  28. 28.
    Wren GG, Kinra VK (1995) Flexural damping of a p55 graphite magnesium composite. J Mater Sci 30:3279–3284.CrossRefGoogle Scholar
  29. 29.
    Zhang Z, Hartwig G (2002) Relation of damping and fatigue damage of unidirectional fibre composite. Int J Fatigue 24:713–718.CrossRefGoogle Scholar

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© Society for Experimental Mechanics 2006

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Procédés de Fabrication (JE 2381)Ecole Nationale Supérieure d’Arts et MétiersChâlons-en-Champagne CedexFrance

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