Effect of Prestresses on the Dispersion of Waves in a System Consisting of a Viscous Liquid Layer and a Compressible Elastic Layer

Abstract

The propagation of acoustic waves in a prestrained compressible elastic layer that interacts with a compressible viscous liquid layer is considered. Use is made of the three-dimensional equations of the linearized theory of finite deformations for the elastic layer and the three-dimensional linearized Navier–Stokes equations for the liquid layer. The problem statement and problem-solving method used are based on the general solutions of the linearized equations for the elastic and liquid layers. A dispersion equation describing the propagation of harmonic waves in the hydroelastic system over a wide frequency range is derived for both thin and thick elastic layers. The effect of the prestresses and the thickness of the layers on the phase velocities and damping factors of modes is analyzed for thin and thick elastic layers. It is established that for all the modes beginning from the second one, there are certain values of fluid thicknesses and frequency at which the pretension in the elastic layer do not affect their phase velocities and damping factors. If the elastic layer is thick, each mode generated by the fluid is shown to have three such frequencies. The approach developed and the results obtained allow us to identify the limits of applicability of models based on various theories of small initial deformations and the ideal-fluid model