Dynamics of contrasted stratified elastic and viscoelastic plates - application to laminated glass

This article deals with the dynamic behavior of highly contrasted stratified (HCS) plate made of elastic or visco-elastic, symmetric or non-symmetric, layers. Such composite structures may correspond to laminates plates or sandwich panels of often use in engineering. The study is based on the synthetic analytical HCS plate model derived by asymptotic approach (Boutin and Viverge 2016). The physical mechanisms within the plate are taken into account by the additional kinematic descriptor constituted by the internal sliding and a bi-torsor formulation. The first part focuses on the elastic HCS plates. After describing the three types of bending waves, and providing a simple assessment of their parameters through Pad'e approximant, the analytical expression of the harmonic Green's function of the HCS plates is established. The classical tools of modal analysis are extended to such plates paying attention to the appropriate boundary conditions. The second part shows that these findings apply to HCS plates with visco-elastic constituents provided that they are expressed in the Fourier domain. This enables to determine the energy loss due to the viscous dissipation. The case of thermo-sensible interlayer is also investigated and the influence of the temperature on the plate behavior is accurately figure out. As a specific example, the laminated glass with PVB interlayer is considered. The damping of the harmonic bending waves is assessed, the procedure to perform a "quasi"-exact modal analysis is detailed and the effect of the temperature on the eigen modes, in terms of frequency and damping, is quantified. Finally, vibrational experiments performed on a laminated glass plate at different temperatures are shown to be in good agreement with the theoretical modeling.