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Chebyshevskii Sbornik, 2021, Volume 22, Issue 3, Pages 423–437
DOI: https://doi.org/10.22405/2226-8383-2018-22-3-423-437
(Mi cheb1082)
 

This article is cited in 3 scientific papers (total in 3 papers)

HISTORY OF MATH AND APPLICATIONS

Reflection and refraction of a plane sound wave in an elastic plate with an inhomogeneous anisotropic coating

L. A. Tolokonnikova, S. L. Tolokonnikovb

a Tula State University (Tula)
b Lomonosov Moscow State University (Moscow)
References:
Abstract: In paper the problem of the reflection and refraction of a plane harmonic sound wave by a homogeneous isotropic elastic plate with an continuously inhomogeneous anisotropic elastic coating is considered.
It is assumed that the plate is adjoin to ideal fluids.
The propagation of small perturbations in a ideal fluid in the case of steady state oscillations is described by Helmholtz's equation. The propagation of elastic waves in a uniform isotropic elastic plate is described by scalar and vector Helmholtz's equations for longitudinal and transverse waves. Oscillations of an inhomogeneous anisotropic elastic coating are described by general motion equations of the continuous medium.
The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement field in inhomogeneous anisotropic coating.
An analytical description of the reflected and transmitted through the plate acoustic fields is obtained.
Particular cases when the material of an inhomogeneous coating is transversely isotropic and isotropic are considered.
The results of numerical calculations of dependence of reflection coefficient of a homogeneous isotropic plate with a transversely isotropic coating from the incidence angle of plane wave are presented.
Keywords: sound waves, reflection and refraction elastic plate, inhomogeneous anisotropic elastic coating.
Funding agency Grant number
Russian Science Foundation 18-11-00199
The research was supported by a grant from the Russian Science Foundation number 18-11-00199, https://rscf.ru/project/18-11-00199/.
Received: 07.06.2021
Accepted: 20.09.2021
Document Type: Article
UDC: 539.3:534.26
Language: Russian
Citation: L. A. Tolokonnikov, S. L. Tolokonnikov, “Reflection and refraction of a plane sound wave in an elastic plate with an inhomogeneous anisotropic coating”, Chebyshevskii Sb., 22:3 (2021), 423–437
Citation in format AMSBIB
\Bibitem{TolTol21}
\by L.~A.~Tolokonnikov, S.~L.~Tolokonnikov
\paper Reflection and refraction of a plane sound wave in an elastic plate with an inhomogeneous anisotropic coating
\jour Chebyshevskii Sb.
\yr 2021
\vol 22
\issue 3
\pages 423--437
\mathnet{http://mi.mathnet.ru/cheb1082}
\crossref{https://doi.org/10.22405/2226-8383-2018-22-3-423-437}
Linking options:
  • https://www.mathnet.ru/eng/cheb1082
  • https://www.mathnet.ru/eng/cheb/v22/i3/p423
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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