On the study of Kirchhoff plates vibration on an acoustic base

Authors

  • Telyatnikov I.S. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russia, Российская Федерация ORCID 0000-0001-8500-2133
  • Kolesnikov M.N. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russia, Российская Федерация ORCID 0000-0002-7552-0567
  • Pavlova A.V. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russia, Российская Федерация ORCID 0000-0002-7729-2860
  • Rubtsov S.E. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russia, Российская Федерация ORCID 0000-0001-7944-0006

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-19-4-91-99

Abstract

In seismology, the study of the wave field on the surface of a medium makes it possible to build models of natural tectonic processes in the Earth's crust and upper mantle. On the scale of the Earth's structure, lithospheric plates can be considered as coatings of relatively small thickness; therefore, a plate can serve as the simplest model of an extended lithospheric structure, which leads to modeling their interactions using separated deformable plates. The problems of geodynamic interaction of deformable plates with acoustic and elastic media can be studied by methods of the contact problems theory. In this paper, we consider a plane problem of steady-state oscillations for a system of two contacting semi-bounded Kirchhoff plates on a layer of an ideal fluid located on a non-deformable foundation. Oscillations are excited by the action of a concentrated harmonic source located in an acoustic medium. The solution is constructed using the integral approach, the eigenfunction method, and the factorization method developed for similar problems arising in geophysics, seismoacoustics, and ecology. We also obtained integral representations of the amplitude values of the coating deflections (the surface displacements of the structure under consideration) and the pressure at the interface between the elastic plates and the liquid medium. The presented approach makes it possible to study the features of the propagation for waves generated by oscillating loads in acoustic media with a coating.

Keywords:

Kirchhoff plates, steady-state oscillations, acoustic medium, concentrated source, eigen function method, factorization method

Acknowledgement

The study was supported by a grant from the Russian Science Foundation and the Kuban Science Foundation (project No. 22-21-20032, https://rscf.ru/project/22-21-20032/).

Author Infos

Ilya S. Telyatnikov

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

e-mail: ilux_t@list.ru

Maksim N. Kolesnikov

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

e-mail: kolesnikov@kubsu.ru

Alla V. Pavlova

д-р физ.-мат. наук, профессор кафедры математического моделирования Кубанского государственного университета

e-mail: pavlova@math.kubsu.ru

Sergeiy E. Rubtsov

канд. физ.-мат. наук, доцент кафедры математического моделирования Кубанского государственного университета

e-mail: rub_serg@mail.ru

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Issue

2022. Vol. 19. No. 4

Section

Mechanics

Pages

91-99

Submitted

2022-11-25

Published

2022-11-30

How to Cite

Telyatnikov I.S., Kolesnikov M.N., Pavlova A.V., Rubtsov S.E. On the study of Kirchhoff plates vibration on an acoustic base. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, vol. 19, no. 4, pp. 91-99. DOI: https://doi.org/10.31429/vestnik-19-4-91-99 (In Russian)

Copyright (c) 2022 Telyatnikov I.S., Kolesnikov M.N., Pavlova A.V., Rubtsov S.E.

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