
This article is cited in 1 scientific paper (total in 1 paper)
Diffraction of a spherical sound wave by an elastic cylinder with an nonuniform coating
L. A. Tolokonnikov^{} ^{} Tula State University
Abstract:
By means of an continuousnonuniform elastic coatings it is
possible to change effectively scattering performances of bodies in
determinate directions if to pick up corresponding the inhomogeneity
laws for mechanical parametres of a coating. In paper the problem
of diffraction of a spherical sound wave by a homogeneous isotropic
elastic cylinder with radially nonuniform elastic coating is
considered. It is believed that an infinite circular cylinder with a
coating is placed in an ideal unlimited fluid, heterogeneity laws of
a coating material are described by differentiable functions, on the
body falls à harmonic spherical sound wave emitted by a point
source. In the case of steady state oscillations the propagation of small
perturbations in ideal fluid is described by the scalar Helmholtz's
equation, and in elastic homogeneous isotropic cylinder — scalar
and vector Helmholtz's equations. The oscillations of an
inhomogeneous isotropic elastic cylindrical layer described by
general motion equations of the continuous medium. The analytical solution of the viewed problem was obtained on the
basis of the known solution for a similar problem of the diffraction
of a plane wave. The velocity potential of a spherical wave is
represented in integral form as a decomposition on wave cylindrical
functions. The integrand turns out to be similar in form to the
expression of the velocity potential of a plane wave. The velocity
potential of the scattered wave in the case of a falling of a
spherical wave on a cylinder with a coating is written as an
integral, the integrand of which is similar in form to the
expression of the potential of the scattered wave when a plane wave
falls on the body. It is necessary to determine the displacement
field in a nonuniform coating to calculate the integrand. For this
the built boundaryvalue problem for the system of ordinary
differential equations of the second order must be solved. The
computational aspects of integral evaluation are considered.
Keywords:
diffraction, sound waves, uniform elastic cylinder, nonuniform elastic coating.
DOI:
https://doi.org/10.22405/222683832018194215226
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UDC:
539.3:534.26 Received: 20.07.2018 Accepted:22.10.2018
Citation:
L. A. Tolokonnikov, “Diffraction of a spherical sound wave by an elastic cylinder with an nonuniform coating”, Chebyshevskii Sb., 19:4 (2018), 215–226
Citation in format AMSBIB
\Bibitem{Tol18}
\by L.~A.~Tolokonnikov
\paper Diffraction of a spherical sound wave by an elastic cylinder with an nonuniform coating
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 4
\pages 215226
\mathnet{http://mi.mathnet.ru/cheb711}
\crossref{https://doi.org/10.22405/222683832018194215226}
\elib{https://elibrary.ru/item.asp?id=36921202}
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http://mi.mathnet.ru/eng/cheb711 http://mi.mathnet.ru/eng/cheb/v19/i4/p215
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This publication is cited in the following articles:

L. A. Tolokonnikov, N. V. Larin, “Rasseyanie tsilindrom s neodnorodnym pokrytiem zvukovykh voln, izluchaemykh lineinym istochnikom, v ploskom volnovode”, Matem. modelirovanie, 33:8 (2021), 97–113

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