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Chebyshevskii Sb., 2019, Volume 20, Issue 2, Pages 311–324 (Mi cheb772)  

This article is cited in 1 scientific paper (total in 1 paper)

The transmission of sound through an elastic plate with an inhomogeneous coating adjoining viscous liquids

L. A. Tolokonnikov, T. S. Nguyen

Tula State University (Tula)

Abstract: In paper the problem of the reflection and transmission of a plane sound wave through a homogeneous elastic plate with an continuously inhomogeneous plate elastic coating adjoining viscous liquids is considered. It is believed that heterogeneity laws of a coating are described by differentiable functions.
The propagation of small perturbations in a viscous fluid in the case of steady state oscillations is described by scalar and vector Helmholtz's equations. The propagation of elastic waves in a uniform isotropic elastic plate is described by two wave equations for longitudinal and transverse waves. Oscillations of an inhomogeneous isotropic 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 coating.
An analytical description of the reflected and transmitted through the plate acoustic fields is obtained.
The results of numerical calculations of dependences of coefficients of reflection and transmission of longitudinal waves from the angle of incidence of plane wave are presented.

Keywords: reflection and transmission of sound waves, homogeneous elastic plate, continuously inhomogeneous coating.

Funding Agency Grant Number
Russian Science Foundation 18-11-00199
The study was carried out for by the grant of Russian scientific Foundation (project 18-11-00199).


DOI: https://doi.org/10.22405/2226-8383-2018-20-2-311-324

Full text: PDF file (1045 kB)
References: PDF file   HTML file

UDC: 539.3:534.26
Received: 12.04.2019
Accepted:12.07.2019

Citation: L. A. Tolokonnikov, T. S. Nguyen, “The transmission of sound through an elastic plate with an inhomogeneous coating adjoining viscous liquids”, Chebyshevskii Sb., 20:2 (2019), 311–324

Citation in format AMSBIB
\Bibitem{TolNgu19}
\by L.~A.~Tolokonnikov, T.~S.~Nguyen
\paper The transmission of sound through an elastic plate with an inhomogeneous coating adjoining viscous liquids
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 2
\pages 311--324
\mathnet{http://mi.mathnet.ru/cheb772}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-2-311-324}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. A. Tolokonnikov, T. Sh. Nguen, “Opredelenie polya smeschenii v neodnorodnom pokrytii uprugoi plastiny pri prokhozhdenii cherez nee ploskoi zvukovoi volny”, Chebyshevskii sb., 21:1 (2020), 289–300  mathnet  crossref
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