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Non-Stationary Plane Problem for a Liquid Layer on a Rigid Base

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An analytical solution is proposed for a plane problem on the action of non-stationary pressure on a layer of compressible fluid. The corresponding linear problem of hydroacoustics is stated. The integral Laplace and Fourier transforms are applied. In the case of a fixed loading domain, the transforms are inverted using tabulated formulas and convolution theorems. As a result, the expressions for speed and pressure at an arbitrary point of the fluid are derived in closed form. The solution is represented as a sum in which the mth term is the mth reflected wave. Retaining a certain finite number of terms in the solution gives the exact solution of the problem on a given time interval taking into account the necessary number of reflected waves. The variation in pressure with time and space coordinates is calculated.

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Authors and Affiliations

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

    V. D. Kubenko

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  1. V. D. Kubenko
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Correspondence to V. D. Kubenko.

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Translated from Prikladnaya Mekhanika, Vol. 55, No. 5, pp. 21–38, September–October 2019.

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Kubenko, V.D. Non-Stationary Plane Problem for a Liquid Layer on a Rigid Base. Int Appl Mech 55, 470–486 (2019). https://doi.org/10.1007/s10778-019-00969-9

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  • DOI: https://doi.org/10.1007/s10778-019-00969-9

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