Effect of an Ideal Liquid Layer on the Surface Instability of an Incompressible Elastic Half-Space with Finite Prestrains

The problem of propagation of normal waves in a prestrained incompressible half-space interacting with a layer of an ideal compressible fluid is studied. The study is based on the three-dimensional linearized equations of the theory of elasticity of finite strains for an incompressible elastic half-space and the three-dimensional linearized Euler equations for an ideal compressible liquid layer. The problem statement and the approach based on the general solutions of the linearized equations for the elastic body and the fluid are applied. A dispersion equation, which describes the propagation of harmonic waves in the hydroelastic system, is obtained. The dispersion curve of a surface wave in a wide frequency range is plotted. The effect of finite prestrains of the elastic half-space and the thickness of the layer of ideal compressible fluid on the phase velocities, the dispersion of surface waves, and the surface instability of the hydroelastic waveguide are analyzed. Numerical results are given in figures and their analysis is given.