On the influence of finite initial deformations on the phase velocities of quasi-Lamb waves in the incompressible elastic layer interacting with the half-space of a viscous compressible fluid

Abstract

The problem of the propagation of quasi-Lamb waves in a pre-deformed incompressible elastic layer that interacts with the half-space of an viscous compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory of finite deformations for the incompressible elastic layer and on the basis of the three-dimensional linearized Navier—Stokes equations for the half-space of a viscous compressible fluid. The problem formulation and the approach, which are based on the utilization of representations of the general solutions of the linearized equations for an elastic solid and a fluid are applied. A dispersion equation, which describes the propagation of normal waves in the hydroelastic system is obtained. The dispersion curves for quasi-Lamb waves over a wide range of frequencies are constructed. The effect of the finite initial deformations in an elastic layer, the thickness of the elastic layer, and the half-space of viscous compressible fluid on the phase velocities, attenuation coefficients, and dispersion of quasi-Lamb modes are analyzed. It is shown that the influence of initial deformations of the elastic layer on the wave process parameters is associated with the localization properties of waves. The approach developed and the results obtained make it possible to establish the limits of applicability of the models, based on different versions of the theory of small initial deformations and the classical elasticity theory for solid bodies, as well the model of an ideal fluid, for the wave processes. The numerical results are presented in the form of graphs, and their analysis is given.