PROBLEM STATEMENT AND METHOD FOR DERIVING THE DISPERSION EQUATION FOR WAVE PROPAGATION IN A THREE-LAYER VISCOELASTIC PLATE WITH A FILLER

Abstract

This article presents the mathematical formulation of the problem of harmonic wave propagation in a three-layer viscoelastic plate with a filler, the solution methodology, and the method for obtaining the dispersion equation. Various contact conditions between the layers (rigid bonding, sliding, elastic connection) are formalized, the Lame equations are reduced, via Green–Lamb potentials, to a system of first-order ordinary differential equations, and a dispersion relation accounting for the viscoelastic properties of the material is derived on the basis of the Rzhanitsyn–Koltunov hereditary kernel. The results obtained serve as the basis for the numerical analysis of wave propagation in three-layer rods and plates presented in subsequent sections.