Non-steady hydroacoustical problem for a fluid of finite depth

1Kubenko, VD
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 2:24-30
Section: Mechanics
Language: Russian

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.

Keywords: acoustical 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.