Non-steady hydroacoustical problem for a fluid of finite depth

TitleNon-steady hydroacoustical problem for a fluid of finite depth
Publication TypeJournal Article
Year of Publication2017
AuthorsKubenko, VD
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published2/2017

An analytic solution of a plane problem on the action of a non-steady pressure on the surface of a flat layer of a fluid is constructed. The integral Laplace and Fourier transformations are applied. In the case of a steady region, where a load acts, the inversion of transformations is executed by means of tabular relations and the appropriate theorems of convolution. As a result, the formula for a pressure at an arbitrary point of the fluid is obtained in the closed form. The solution is presented in the form of a sum, whose m-term represents the m-th reflected wave. The retention of a certain number of terms in the solution gives the exact solution of the problem on the given time interval with regard for the necessary number of waves.

Keywordsacoustical wave, liquid layer, non-steady loading
  1. Morse, P. M., Feshbach, H. (1953). Methods of Theoretical Physics. In 2 Vol. Part 1. New York: McGraw-Hill.
  2. Ditkin, V. A., Prudnikov, A. P. (1961). Integral Transforms and Operational Calculation, Moscow: GIFML (in Russian).
  3. M., Abramovitz, I. A., Stegun (Eds.). (1964). Handbook of Mathematical Functions. New York: Nat. Bureau of Standards.