<p>An analytical solution has been obtained for the plane problem describing a layer of ideal compressible liquid resting on a rigid surface subjected to a suddenly applied velocity perturbation. Laplace and Fourier integral transforms have been used to derive expressions for the velocity and pressure fields in the frequency domain. The original functions have been recovered using tabulated relations and the convolution theorem. As a result, the exact analytical expressions for pressure and velocity have been obtained in the time domain in the form of series, where each successive term describes a subsequent reflected wave. These expressions have made it possible to evaluate the characteristics of the wave field at the arbitrary point of the liquid layer for various types of non-stationary load. In the case where the excitation suddenly occurs on the fixed region of the bottom, the velocities in the near-field and far-field zones have been calculated as an example.</p>

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Non-stationary Kinematic Excitation of Bottom of Liquid Layer: Plane Problem

  • V. D. Kubenko

摘要

An analytical solution has been obtained for the plane problem describing a layer of ideal compressible liquid resting on a rigid surface subjected to a suddenly applied velocity perturbation. Laplace and Fourier integral transforms have been used to derive expressions for the velocity and pressure fields in the frequency domain. The original functions have been recovered using tabulated relations and the convolution theorem. As a result, the exact analytical expressions for pressure and velocity have been obtained in the time domain in the form of series, where each successive term describes a subsequent reflected wave. These expressions have made it possible to evaluate the characteristics of the wave field at the arbitrary point of the liquid layer for various types of non-stationary load. In the case where the excitation suddenly occurs on the fixed region of the bottom, the velocities in the near-field and far-field zones have been calculated as an example.