Title | Non-steady hydroacoustical problem for a fluid of finite depth |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | Kubenko, VD |

Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |

DOI | 10.15407/dopovidi2017.02.024 |

Issue | 2 |

Section | Mechanics |

Pagination | 24-30 |

Date Published | 2/2017 |

Language | Russian |

Abstract | 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 |

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