On the influence of a layer of a viscous compressible fluid on the surface instability of the incompressible elastic half-plane exposed to finite initial deformations

Bagno, AM
Dopov. Nac. akad. nauk Ukr. 2020, 4:25-33
https://doi.org/10.15407/dopovidi2020.04.025
Section: Mechanics
Language: Russian
Abstract: 

The problem of propagation of harmonic waves in the pre-deformed incompressible elastic half-space that interacts with a layer of an viscous compressible fluid is considered. The study is based on the three-dimensional linearized equations of theory of elasticity of finite deformations for the incompressible elastic half-space and the three-dimensional linearized Navier—Stokes equations for a layer of a viscous compressible fluid. The approach based on the utilization of representations of general solutions of the linearized equations for an elastic solid and a fluid is applied. A dispersion equation, which describes propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curve for surface waves over a wide range of frequencies is constructed. The effects of finite initial deformations of the elastic half-space and of the thickness of the layer of a viscous compressible fluid on the phase velocities, attenuation coefficients, dispersion of the surface waves, and surface instability of a hydroelastic waveguide are analyzed. The numerical results are presented in the form of graphs, and their analysis is given.

Keywords: attenuation coefficient, finite initial deformations, incompressible elastic half-space, layer of viscous compressible fluid, phase velocity, surface instability, surface waves
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