Scattering of sound waves by an cylinder with an radial non-uniform elastic coating in a planar waveguide
L. A. Tolokonnikov
Tula state University, Tula
In paper the problem of sound wave scattering by absolutely rigid
cylinder with radially inhomogeneous isotropic elastic coating in a
planar waveguide is considered. It is believed that a waveguide
filled with a homogeneous ideal fluid, one of its borders is
absolutely rigid and the other — acoustically soft, heterogeneity
laws of a coating material are described by differentiable
functions, harmonic sound wave excited by a given distribution of
sources in the section waveguide.
In the case of steady state oscillations the propagation of small
perturbations in ideal fluid is described by the Helmholtz's
equation. The oscillations of an inhomogeneous isotropic elastic
cylindrical layer described by general motion equations of the
The boundary-value problem for the system of ordinary second order
differential equations is constructed for determination of the
displacement field in inhomogeneous coating.
The primary field of disturbances is represented by a set of its own
waveguide waves. The pressure of the field scattered by the cylindrical body is sought as potential
of a simple layer.
The Green function for the Helmholtz equation that satisfies the
given boundary conditions on the waveguide walls and conditions of
radiation at infinity is constructed. The function of distribution
density of sources are sought as a Fourier series expansion. The
infinite linear system of equations is obtained for determination of
the coefficients of this decomposition. The solution of truncated
infinite system is found by the inverse matrix method.
Analytical expressions for the scattered acoustic field in
different areas of the waveguide are obtained.
scattering, sound waves, cylinder, non-uniform elastic coating, planar waveguide.
|Russian Science Foundation
|The study was carried out at the expense of a grant from the Russian science Foundation (project 18-11-00199).
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L. A. Tolokonnikov, “Scattering of sound waves by an cylinder with an radial non-uniform elastic coating in a planar waveguide”, Chebyshevskii Sb., 20:1 (2019), 272–283
Citation in format AMSBIB
\paper Scattering of sound waves by an cylinder with an radial non-uniform elastic coating in a~planar waveguide
\jour Chebyshevskii Sb.
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