Geodesic
Diffraction of sound waves on an inhomogeneous thick-walled elastic cylindrical shell of finite length
Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 274-288

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The article considers the diffraction of sound waves by an inhomogeneous isotropic cylindrical shell of finite length of arbitrary thickness. It is assumed that there is a vacuum in the cavity of the cylindrical shell. The density and elastic modulus of the shell material are described by continuous functions of the radial coordinate. The primary field of disturbances is a plane harmonic sound wave falling obliquely on the body. For the scattered field, a representation in the form of the Helmholtz-Kirchhoff integral is used. It is shown that the use of quadrature formulas for parallelepipedal Korobov grids makes it possible to reduce the number of calculations with approximate calculation of integrals. This method is compared with the calculation of integrals by the method of sequential integration using the quadrature formula of trapezoids. The calculation time of the field potential scattered by a finite cylindrical shell is compared by two methods of calculating integrals. A significant effect of the inhomogeneity of the shell material on the sound-reflecting properties of elastic cylindrical bodies has been revealed.
Keywords: scattering, sound waves, a finite cylindrical shell, quadrature formulas, periodization, parallelepipedal Korobov grids. 
@article{CHEB_2023_24_5_a21,
     author = {N. N. Dobrovol'skii and D. Yu. Efimov and L. A. Tolokonnikov},
     title = {Diffraction of sound waves on an inhomogeneous thick-walled elastic cylindrical shell of finite length},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {274--288},
     publisher = {mathdoc},
     volume = {24},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a21/}
}
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N. N. Dobrovol'skii; D. Yu. Efimov; L. A. Tolokonnikov. Diffraction of sound waves on an inhomogeneous thick-walled elastic cylindrical shell of finite length. Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 274-288. http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a21/