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Effect of Finite Initial Strains on the Wave Process in the System of an Incompressible Half-Space and an Ideal Liquid Layer*

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The problem of propagation of normal waves in a prestrained incompressible half-space interacting with a layer of a compressible ideal fluid is considered. 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 a compressible ideal fluid. 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 curves of normal waves in a wide range of frequencies are plotted. The effect of finite initial strains of the elastic half-space and the thickness of the layer of compressible ideal fluid on the phase velocities of harmonic waves is analyzed. The effect of the initial strains of the elastic half-space on the parameters of the wave process is related to the properties of wave localization. The criterion of the existence of normal waves in hydroelastic waveguides is proposed. It is shown that finite initial strains can significantly change the nature of the wave process in the hydroelastic system. The developed approach and the obtained results allow us to determine the limits of application of models of wave processes based on different variants of the theory of small initial strains and the classical theory of elasticity for a solid body. Numerical results are given in the form of graphs and analyzed.

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    O. M. Bagno

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  1. O. M. Bagno
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Correspondence to O. M. Bagno.

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* This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).

Translated from Prykladna Mekhanika, Vol. 57, No. 6, pp. 30–44, November–December 2021.

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Bagno, O.M. Effect of Finite Initial Strains on the Wave Process in the System of an Incompressible Half-Space and an Ideal Liquid Layer*. Int Appl Mech 57, 644–654 (2021). https://doi.org/10.1007/s10778-022-01114-9

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  • DOI: https://doi.org/10.1007/s10778-022-01114-9

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