Diffraction of a plane sound wave by an elastic sphere with an non-uniform coating located near a plane
https://doi.org/10.22405/2226-8383-2018-19-2-199-216
Abstract
In paper the problem of diffraction of a plane sound wave by a
homogeneous elastic sphere with radially non-uniform elastic coating
located near a plane. It is necessary that the body is placed in an
ideal fluid, the spreading flat surface is absolutely rigid and
absolutely soft, heterogeneity laws of a coating material are
described by continuous functions.
The problem is replaced by a problem of diffraction on two bodies.
According to a method of imaginary radiants the dividing boundary of
mediums is substituted by with mirrorly mapped imaginary sphere
which is situated in the field of two plane waves. The analytical
solution of the problem of diffraction of a plane sound wave by two
identical homogeneous elastic spheres with radially non-uniform
coatings situated in an ideal unlimited fluid is received. For
solution of the problem the addition theorem for spherical wave
functions is used. Analytic expressions In the form of decomposition
on spherical functions are obtained which describe the wave fields
in the containing medium and the homogeneous elastic bodies. The
boundary-value problem for the system of ordinary differential
equations of the second order is constructed for determination of
the displacement fields in non-uniform coatings. On the basis of
solution of problem of diffraction a plane wave by two bodies the
diffraction problem for case of scattering of second plane wave is
received. By summation of results of solutions of two diffraction
problems the analytical solution of the problem of diffraction of a
plane sound wave by a elastic sphere with coating located near a
plane is received.
By means of an continuous-non-uniform 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.
About the Author
Lev Alekseevich Tolokonnikov
Tula State University.
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor, department of
applied mathe\-matics and computer science
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Review
For citations:
Tolokonnikov L.A. Diffraction of a plane sound wave by an elastic sphere with an non-uniform coating located near a plane. Chebyshevskii Sbornik. 2018;19(2):199-216. (In Russ.) https://doi.org/10.22405/2226-8383-2018-19-2-199-216
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