^{1}Kubenko, VD^{1}S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv |

Dopov. Nac. akad. nauk Ukr. 2017, 2:24-30 |

https://doi.org/10.15407/dopovidi2017.02.024 |

Section: Mechanics |

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 |

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