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

The propagation of normal waves in a prestrained incompressible half-space interacting with a layer of a viscous compressible fluid is studied. The study is based on the three-dimensional linearized equations of elasticity for the incompressible elastic half-space and the three-dimensional linearized Navier–Stokes equations for the viscous compressible liquid layer. A problem statement and an approach based on the general solutions of the linearized equations for the elastic body and the fluid are applied. A dispersion equation that describes the propagation of harmonic waves in the hydroelastic system is derived. The dispersion curves of surface waves in a wide range of frequencies are plotted. The effect of the finite prestrains of the elastic half-space and the thickness of the layer of viscous compressible fluid on the phase velocities, the dispersion of surface waves, and the surface instability of the hydroelastic waveguide are analyzed. Numerical results are plotted and analyzed.