International Applied Mechanics

, Volume 55, Issue 5, pp 470–486 | Cite as

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

  • V. D. KubenkoEmail author

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.


non-stationary loading acoustical waves liquid layer 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

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