THE VIRTUAL FIELDS METHOD

- Grédiac M., Paris P.-A.,
Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects,
*Journal of Sound and Vibration*, vol. 195, pp. 401–415, 1996. - Grédiac M., Fournier N., Paris P.-A., Surrel Y.,
Direct identification of elastic constants of anisotropic
plates by modal analysis: experiments and results,
*Journal of Sound and Vibration*, vol. 210, pp. 645–659, 1998. - Grédiac M., Fournier N., Paris P.-A., Surrel Y.,
Direct measurement of invariant parameters of composite plates,
*Journal of Composite Materials*, vol. 33, pp. 1939–1965, 1999.

The following slideshow explains how the method works. Application to vibrating plates

There are two main advantages to the proposed procedure. First, both complex stiffnesses are identified simultaneously at a given frequency, ie, the Qxx and Qxy components, but also the two associated loss stiffnesses Bxx and Bxy. Since most of the alternative methods rely on beam specimens, the Bxy parameter cannot usually be measured. The second advantage is that the damping measurements are not affected by dissipation occuring at the support points. Indeed, the method considers a part of the plate that does not contain external forces and writes that the material is at equilibrium (equilibrium between the inertial and viscoelastic forces). This is independent from what happens at the contact zone. For instance, it has been shown that an increase of structural damping (obtained by inserting a rubber washer at the clamping point of the tested plate) did not change the identified parameters (stiffness and damping). Results are shown in the the following document: test with and without rubber washers.

Clearly, it is possible to apply the method to other tests such as heterogeneous creep or relaxation tests although this has not been done yet.

- Giraudeau A., Pierron F.,
Simultaneous identification of stiffness and damping properties of isotropic materials from forced vibrating plates,
*Comptes rendus Mécanique*, vol. 331, n° 4, pp. 259-264, 2003. - Giraudeau A., Pierron F.,
Identification of stiffness and damping properties of thin isotropic vibrating plates using the Virtual Fields Method. Theory and simulations,
*Journal of Sound and Vibration*, vol. 284, n° 3-5, pp. 757-781, 2005. - Giraudeau A., Guo B., Pierron F.,
Stiffness and damping identification from full field measurements on vibrating plates,
*Experimental Mechanics*, vol. 46, n° 6, pp. 777-787, 2006. - Giraudeau A., Pierron F., Guo B., An alternative to modal analysis for material stiffness and damping identification from vibrating plates, Journal of Sound and Vibration, vol. 329, n° 10, pp. 1653-1672, 2010.