Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2018, Volume 19, Issue 1, Pages 220–237 (Mi cheb633)  

Scattering of sound waves by an elastic ellipsoid with an inhomogeneous coating in the half-space with ideal surface

S. A. Skobel'tsyn

Tula State University

Abstract: The solution of the diffraction problem for a plane sound wave on an elastic ellipsoid $E$ with an outer inhomogeneous layer is presented. The ellipsoid is in a half-space filled with an ideal fluid. The boundary of a half-space $\Pi$ is an acoustically rigid or acoustically soft surface.
To obtain a solution, the area occupied by the liquid is expanded to full space. An additional scattering obstacle is introduced. This obstacle is a copy of $E$, located mirror-wise with respect to the plane $\Pi$. A second incident plane wave is also added. This wave ensures the fulfillment of that condition at the points of the plane $\Pi$, which corresponds to the type of the half-space boundary in the initial formulation of the problem.
Thus, the problem is transformed into the problem of scattering of two plane sound waves on two ellipsoids in unbounded space.
The solution is based on the linear theory of elasticity and the model of propagation of small vibrations in an ideal fluid. In the outer part of the environment, the solution is sought analytically in the form of an expansion in spherical harmonics and Bessel functions. In the spherical region, which includes two ellipsoids and an adjacent layer of liquid, the finite element method (FEM) is used.
The results of the calculation of the directivity patterns of the scattered sound field in the far zone are presented. These dependences show the influence of the geometric and material parameters of the ellipsoid on the diffraction of sound.

Keywords: scattering of sound waves, half-space, inhomogeneous elastic ellipsoid, finite element method.

Funding Agency Grant Number
Russian Science Foundation 18-11-00199


DOI: https://doi.org/10.22405/2226-8383-2018-19-1-220-237

Full text: PDF file (1086 kB)
References: PDF file   HTML file

UDC: 539.3

Citation: S. A. Skobel'tsyn, “Scattering of sound waves by an elastic ellipsoid with an inhomogeneous coating in the half-space with ideal surface”, Chebyshevskii Sb., 19:1 (2018), 220–237

Citation in format AMSBIB
\Bibitem{Sko18}
\by S.~A.~Skobel'tsyn
\paper Scattering of sound waves by an elastic ellipsoid with an inhomogeneous coating in the half-space with ideal surface
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 1
\pages 220--237
\mathnet{http://mi.mathnet.ru/cheb633}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-1-220-237}
\elib{https://elibrary.ru/item.asp?id=36312688}


Linking options:
  • http://mi.mathnet.ru/eng/cheb633
  • http://mi.mathnet.ru/eng/cheb/v19/i1/p220

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:198
    Full text:59
    References:17

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021