Effect of Prestresses on Quasi-Lamb Waves in a System Consisting of a Compressible Viscous Liquid Half-Space and an Elastic Layer

Abstract

The problem of propagation quasi-Lamb waves in a prestrained elastic layer interacting with a half-space of compressible viscous fluid is considered. The problem is solved using the three-dimensional linearized equations of theory of finite deformations for the elastic layer and the three-dimensional linearized Navier–Stokes equations for the compressible viscous fluid. A problem statement and approach based on the general solutions of linearized equations for the elastic body and fluid are used. The dispersion equations describing the propagation of quasi-Lamb waves in hydroelastic systems over wide range of frequencies are derived. The effect of the initial stresses and the thickness of the elastic layer and compressible viscous liquid half-space on the phase velocities and damping factors of quasi-Lamb modes are analyzed. The approach developed and the results obtained make it possible to establish the limits of applicability of the models for wave processes, based on different versions of the theory of small initial deformations, the classical theory of elasticity, and the model of ideal fluid. The numerical results are presented in the form of graphs and analyzed.