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 Matem. Mod., 2019, Volume 31, Number 5, Pages 20–38 (Mi mm4070)

Sound scattering by the thermoelastic continuously-inhomogeneous covered sphere in heat-conducting fluid

N. V. Larin, L. A. Tolokonnikov

Tula State University, Tula region

Abstract: In the project we solved direct and inverse problems of the plane harmonic acoustic wave diffraction on the thermoelastic sphere covered with radially inhomogeneous thermoelastic spherical layer, bounded by inviscid heat-conducting fluid. Coated ball vibrations are considered in terms of the linear model of coupled thermoelasticity. The wave fields are defined in a spherical body and outside it. The results of calculations of the frequency and angular dependences of the amplitude of the scattered acoustic field in the far zone are presented. We showed the essential difference between the characteristics of sound scattering for thermoelastic and elastic bodies. In the project we modeled the coating, which provides the smallest scattering of a sound in a given frequency range and angular observation sector. Functionals expressing the intensity of sound reflection were constructed, as well as an algorithm for its minimization. The algorithm is based on the combination of random search and coordinate descent methods. We discovered the inhomogeneity laws of the thermoelastic coating with optimal sound-reflecting properties.

Keywords: direct and inverse problems of diffraction, acoustic wave, thermoelastic sphere, inhomogeneous thermoelastic layer, heat-conducting fluid.

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

DOI: https://doi.org/10.1134/S0234087919050022

Full text: PDF file (434 kB)
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Revised: 06.11.2018
Accepted:10.12.2018

Citation: N. V. Larin, L. A. Tolokonnikov, “Sound scattering by the thermoelastic continuously-inhomogeneous covered sphere in heat-conducting fluid”, Matem. Mod., 31:5 (2019), 20–38

Citation in format AMSBIB
\Bibitem{LarTol19} \by N.~V.~Larin, L.~A.~Tolokonnikov \paper Sound scattering by the thermoelastic continuously-inhomogeneous covered sphere in heat-conducting fluid \jour Matem. Mod. \yr 2019 \vol 31 \issue 5 \pages 20--38 \mathnet{http://mi.mathnet.ru/mm4070} \crossref{https://doi.org/10.1134/S0234087919050022} \elib{https://elibrary.ru/item.asp?id=37298171}