Dispersion of elastic waves in laminated glass

Elastic sandwich-type structures with high-contrast material and geometrical properties have numerous applications in modern engineering, including, in particular, laminated glass, photovoltaic panels, precipitator plates in gas filters, etc. Multi-parametric modelling of such structures assumes taking into consideration various types of contrast in stiffness, density and thickness. The present contribution is concerned with analysis of low-frequency dispersion of elastic waves in case of an antisymmetric motion of a three-layered symmetric plate, modelling laminated glass. The conditions on material and geometrical parameters, leading to the lowest non-zero thickness shear resonance frequency tending to zero, are formulated. In this case the dispersion relation possesses two low-frequency modes instead of a single fundamental low-frequency mode, which is typical for a homogeneous plate. A two-mode uniform asymptotic approximation is constructed, along with local approximations for the fundamental mode and the first shear harmonic