On the influence of finite initial deformations on parameters of a wave process in the system consisting of an ideal fluid layer and the elastic halfspace

1Bahno, OM
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 2:31-39
https://doi.org/10.15407/dopovidi2019.02.031
Section: Mechanics
Language: Russian
Abstract: 

The problem of propagation of normal waves in a predeformed incompressible elastic halfspace that interacts with a layer of an ideal compressible fluid is considered. The study is conducted on the basis of the threedimensional linearized equations of elasticity theory of finite deformations for the incompressible elastic halfspace and on the basis of the threedimensional linearized Euler equations for an ideal compressible fluid. The statement of the problem and the approach based on the use of representations of general solutions of the linearized equations for an elastic solid and a fluid are applied. A dispersion equation, which describes the propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curves for normal waves over a wide range of frequencies are constructed. The effect of finite initial deformations of the elastic halfspace and of the thickness of the layer of an ideal compressible fluid on the phase velocities of harmonic waves are analyzed. A criterion for the existence of normal waves in hydroelastic waveguides is proposed. For the wave processes, an approach developed and the results obtained make it possible to establish the limits of applicability of the models based on different versions of the theory of small initial deformations and of the classical elasticity theory for a solid body. The numerical results are presented in the form of graphs, and their analysis is given.

Keywords: incompressible elastic halfspace, initial deformations, layer of an ideal compressible fluid, normal waves, phase velocity
References: 

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