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. 
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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/

[1] Williams W. E., Lighthill M. J., “Diffraction by a cylinder of finite length”, Math. Proceed. Camb. Phil. Soc., 52:2 (1956), 322–335 | DOI | MR

[2] Lyamshev, L. M., “Sound diffraction on a thin bounded elastic cylindrical shell”, Dokl. Akad. Nauk SSSR, 115:2 (1957), 271–273 (in Russian) | MR | Zbl

[3] Lyamshev, L. M., “Sound scattering by a thin rod of finite length”, Akust. Zhurnal, 4:1 (1958), 51–58 (in Russian) | MR

[4] Andreeva, I. B., Samovol'kin, V. G., “Sound scattering by elastic cylinders of finite length”, Akust. Zhurnal, 22:5 (1976), 637–643 (in Russian)

[5] Su J. -H., Varadan V. V., Varadan V. K., Flax L., “Acoustic wave scattering by a finite elastic cylinder in water”, J. Acoust. Soc. Amer., 68:2 (1980), 686–691 | DOI | MR | Zbl

[6] Muzychenko, V. V., Rybak, S. A., “Amplitude of resonant sound scattering by a finite cylindrical shell in a liquid”, Akust. Zhurnal, 32:1 (1986), 129–131 (in Russian)

[7] Muzychenko, V. V., Rybak, S. A., “Some features of sound scattering by finite cylindrical shells”, Akust. Zhurnal, 32:5 (1986), 699–701 (in Russian)

[8] Belogortsev, A. S., Muzychenko, V. V., “Influence of a restriction of a cylindrical shell on a backscattering amplitude”, Akust. Zhurnal, 37:2 (1991), 228–234 (in Russian)

[9] Dotsenko, I. E., Muzychenko, V. V., Rybak, S. A., “Sound scattering on the limited elastic cylindrical shell with semispherical endings”, Akust. Zhurnal, 37:5 (1991), 922–932 (in Russian)

[10] Shenderov, E. L., Radiation and Scattering of Sound, Sudostroenie, L., 1989, 302 pp. (in Russian)

[11] Lebedev, A. V., Khil'ko, A. I., “Sound scattering by limited length elastic cylindrical shells with thin walls”, Akust. Zhurnal, 38:6 (1992), 1057–1065 (in Russian)

[12] Belogortsev, A. S., Bugayev, V. V., Muzychenko, V. V., “Sound scattering on the limited elastic cylindrical shell with semispherical endings”, Akust. Zhurnal, 39:4 (1991), 598–604 (in Russian)

[13] Kosarev, O. I., “Secondary hydroacoustic field generated by a solid finite cylinder in the far field”, Probl. Mashinostr. Avtom., 2015, no. 4, 99–103 (in Russian)

[14] Kosarev, O. I., “Diffraction of sound by a hard cylinder of finite length in the far field”, Vestn. Nauchno-Tekh. Razvit., 2017, no. 3(115), 30–37 (in Russian) | Zbl

[15] Tolokonnikov, L. A., Efimov, D. Yu., “Scattering of Sound Waves by a Finite Length Elastic Cylinder with an Inhomogeneous Coating”, Mathematical Models and Computer Simulations, 15:5 (2023), 863–876 | DOI | DOI | MR | Zbl

[16] Shenderov, E. L., Wave problems of underwater acoustics, Sudostroenie, L., 1972, 352 pp. (in Russian)

[17] Ivanov, E. A., Diffraction of electromagnetic waves by two bodies, Nauka i tekhnika, Minsk, 1968, 584 pp. (in Russian)

[18] Nowacki, W., Teoria sprezystosci, PWN, Warszawa, 1973 | MR

[19] Kurant, R., Partial Differential Equations, Mir, M., 1964, 830 pp. (in Russian)

[20] Lebedev, N. N., Special Functions and their Applications, Fizmatgiz, M., 1963, 358 pp. (in Russian)

[21] Kalitkin, N. N., Numerical methods, Fizmatgiz, M., 1978, 512 pp. (in Russian)

[22] Zavyialov, Yu. S., Kvasov, B. I., Miroshnichenko, V. L., Spline function methods, Nauka, M., 1980, 352 pp. (in Russian) | MR

[23] Veksler, N. D., Korsunskii, V. M., Rybak, S. A., “Scattering of an obliquely incident plane acoustic wave by circular cylindrical shell”, Akust. Zhurnal, 36:1 (1990), 12–16 (in Russian)

[24] Korobov, N. M., Number-theoretic methods in approximate analysis, 2nd ed., MTSNMO, M., 2004

[25] Dobrovol'skii, N. N., Skobel'tsyn, S. A., Tolokonnikov, L. A., Larin, N. V., “About application of number-theoretic grids in problems of acoustics”, Chebyshevskii sbornik, 22:3 (2021), 368–382 (in Russian) | DOI | Zbl