To the study of Kirchhoff plates vibration on a hydroelastic foundation

Authors

  • Kolesnikov M.N. Kuban State University, Krasnodar, Russian Federation ORCID 0000-0002-7552-0567
  • Telyatnikov I.S. Kuban State University, Krasnodar; Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Rostov-on-Don, Russian Federation ORCID 0000-0001-8500-2133

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-21-3-16-25

Abstract

The problem of studying the wave fields on the surface of geological structures is relevant in cases of monitoring dangerous endogeodynamic processes and unfavorable exogenous processes, as well as determining their connection with the tectonic behavior of territories. In this paper we consider the problem of oscillations for a liquid layer between elastic structures caused by a localized vibration source immersed in the liquid. The coating is modeled by a system of contacting extended plates with parameters averaged by thickness. By using the integral approach, we reduced the problem of oscillations for a hydroelastic structure to a functional equation relative to the Fourier images of the displacements for the coating plates, which is solved using the Wiener-Hopf method. In matters of seismology, the study of the wave field on the surface of the medium allows us to construct models of natural tectonic processes and assess the possible consequences caused by buried sources. The presented approach can be used to study the characteristics of wave processes in hydroelastic media modeled by a multilayer foundation containing immersed liquid layers.

Keywords:

steady-state oscillations, Kirchhoff plates, acoustic medium, elastic base, concentrated source, factorization method

Acknowledgement

The study was supported by a grant from the Russian Science Foundation and the Kuban Science Foundation No. 24-21-20032.

Author Infos

Maxim N. Kolesnikov

канд. физ.-мат. наук, научный сотрудник Научно-исследовательской части Кубанского государственного университета

e-mail: kolesnikov@kubsu.ru

Ilya S. Telyatnikov

канд. физ.-мат. наук, научный сотрудник Научно-исследовательской части Кубанского государственного университета, старший научный сотрудник Южного научного центра РАН

e-mail: ilux_t@list.ru

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Issue

2024. Vol. 21. No. 3

Section

Mechanics

Pages

16-25

Submitted

2024-08-19

Published

2024-09-24

How to Cite

Kolesnikov M.N., Telyatnikov I.S. To the study of Kirchhoff plates vibration on a hydroelastic foundation. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2024, vol. 21, no. 3, pp. 16-25. DOI: https://doi.org/10.31429/vestnik-21-3-16-25 (In Russian)

Copyright (c) 2024 Kolesnikov M.N., Telyatnikov I.S.

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