On the effect of finite initial deformations on the phase velocities of normal waves in the elastic half-space interacting with the layer of an ideal compressible fluid

1Bahno, OM
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 1:23-32
https://doi.org/10.15407/dopovidi2019.01.023
Section: Mechanics
Language: Russian
Abstract: 

The problem of propagation of normal waves in a pre-deformed elastic half-space that interacts with the layer of an ideal compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory for finite deformations in the compressible and incompressible elastic half-spaces and on the basis of the three-dimensional linearized Euler equations for an ideal compressible fluid. The problem formulation and the approach based on the utilization of representations of general solutions of the linearized equations for elastic solid and fluid are applied. The dispersion equations, which describe the propagation of harmonic waves in hydroelastic systems, are obtained. The dispersion curves for normal waves over a wide range of frequencies are constructed. The effects of finite initial deformations of the elastic half-space and the thickness of the layer of an ideal compressible fluid on the phase velocities of harmonic waves are analyzed. It is shown that the influence of initial deformations of the elastic half-space on the wave process parameters is associated with the localization properties of waves. A criterion for the existence of the normal waves in hydroelastic waveguides is proposed. The approach developed and the results obtained make it possible to establish, for the wave processes, the limits of applicability of the models based on different versions of the theory of small initial deformations and the classical elasticity theory for a solid body. The numerical results are presented in the form of graphs, and their analysis is given.

Keywords: compressible and incompressible elastic half-spaces, dispersion of waves, initial stresses, layer of an ideal compressible fluid, normal waves
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