The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT

This work studies the effect of a three-variable viscoelastic foundation on wave propagation in functionally graded (FG) sandwich plates using a simple quasi-3D plate theory. The presented solution is based on a four-unknown plate theory that simplifies the calculations and considers the stretching effect. The theory employs a simple sinusoidal function for the shear deformation shape. The studied plates are composite sandwiches in which the layers are ceramic, metal, or FG ceramic-metal. The governing differential equations are obtained for the proposed quasi-3D plate theory using Hamilton's principle. The eigenvalue problem is formulated for the wave propagation and solved for the studied desperation relations. Finally, new results that examine the influences of the foundation parameters, the FGM exponent and the core-to-thickness ratio on the various dispersion relations of wave propagation are presented.