Scattering of Acoustic Waves by an Inhomogeneous Elastic Cylindrical Shell of Finite Length in a Half-Space

D. Yu. Efimov; Ефимов Д. Ю.

doi:10.31857/S0032823524020096

Scattering of Acoustic Waves by an Inhomogeneous Elastic Cylindrical Shell of Finite Length in a Half-Space

Authors: Efimov D.Y.¹
Affiliations:
1. Tula State University
Issue: Vol 88, No 2 (2024)
Pages: 299-312
Section: Articles
URL: https://ruspoj.com/0032-8235/article/view/675069
DOI: https://doi.org/10.31857/S0032823524020096
EDN: https://elibrary.ru/XUEOPA
ID: 675069

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract

An analytical solution to the problem of diffraction of a plane acoustic wave on a radially inhomogeneous thick-walled elastic cylindrical shell of finite length is obtained. The cylindrical shell is located in an acoustic half-space filled with an ideal liquid. The boundary of the half-space is an acoustically rigid or acoustically soft surface. The results of calculations of the acoustic field in the far zone are presented.

Keywords

sound diffraction, inhomogeneous elastic shell, flat surface

Full Text

About the authors

D. Yu. Efimov

Tula State University

Author for correspondence.
Email: bogart.efimov@yandex.ru
Russian Federation, Tula

References

Tolokonnikov L.A. Scattering of an obliquely incident plane sound wave by an elastic cylinder with a non-uniform covering // Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, 2013, no. 2–2, pp. 265–274. (in Russian)
Tolokonnikov L.A., Efimov D.Yu. Diffraction of cylindrical sound waves by an elastic cylinder with a radially inhomogeneous coating // Chebyshev. sb., 2021, vol. 22, no. 1, pp. 460–472. (in Russian)
Tolokonnikov L.A. Diffraction of a spherical sound wave by an elastic cylinder with an non-uniform coating // Chebyshev. sb., 2018, vol. 19, no. 4, pp. 215–226. (in Russian)
Kuznetsov S.V., Ilyashenko A.V. Polarization of Pochhammer–Chree waves: axisymmetric longitudinal modes // Acoust. Phys., 2018, vol. 64, no. 6, pp. 659–664.
Ilyashenko A.V. Pochhammer–Cree longitudinal waves: Anomalous polarization // Mech. Solids. 2019. vol. 54. pp. 598–606.
Tolokonnikov L.A., Efimov D.Yu. Scattering of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surface // Chebyshev. sb., 2020, vol. 21, no. 4, pp. 369–381. (in Russian)
Wai Keung Lui, Kai Ming Li. The scattering of sound by a long cylinder above an impedance boundary // J. Acoust. Soc. Amer., 2010, vol. 127, no. 2, pp. 664–674.
Shenderov E.L. Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace // Acoust. Phys., 2002, vol. 48, no. 2, pp. 225–234.
Tolokonnikov L.A., Efimov D.Yu. Diffraction of sound waves at an elastic cylinder with an inhomogeneous coating in the vicinity of the boundary of an elastic half-space // Mech. of Solids, 2021, vol. 56, no. 8, pp. 1657–1667.
Williams W.E. Diffraction by a cylinder of finite length // Math. Proc. Camb. Phil. Soc., 1956, vol. 52, no. 2, pp. 322–335.
Kosarev O.I. Secondary hydroacoustic field generated by a solid finite cylinder in the far field // Probl. Mashinostr. Avtom., 2015, no. 4, pp. 99–103. (in Russian)
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), pp. 30–37. (in Russian)
Lyamshev L.M. Sound diffraction on a thin bounded elastic cylindrical shell // Dokl. AN SSSR, 1957, vol. 115, no. 2, pp. 271–273. (in Russian)
Lyamshev L.M. Sound scattering by a thin rod of finite length // Akust. zh., 1958, vol. 4, no. 1, pp. 51–58. (in Russian)
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., 1980, vol. 68, no. 2, pp. 686–691.
Muzychenko V.V., Rybak S.A. Amplituda rezonansnogo rasseyaniya zvuka ogranichennoy tsilindricheskoy obolochkoy v zhidkosti // Akust. zh., 1986, vol. 32, no. 1, pp. 129–131. (in Russian)
Muzychenko V.V., Rybak S.A. Nekotoryye osobennosti rasseyaniya zvuka ogranichennymi tsilindricheskimi obolochkami // Akust. zh., 1986, vol. 32, no. 5, pp. 699–701. (in Russian)
Belogortsev A.S., Muzychenko V.V. Vliyanie ogranichennosti tsilindricheskoy skorosti na velichinu obratnogo rasseyaniya // Akust. zh., 1991, vol. 37, no. 2, pp. 228–234. (in Russian)
Dotsenko I.E., Muzychenko V.V., Rybak S.A. Rasseyaniye zvuka na ogranichennoy tsilindricheskoy uprugoy obolochke s polusfericheskimi zaglushkami // Akust. zh., 1991, vol. 37, no. 5, pp. 922–932. (in Russian)
Tolokonnikov L.A., Efimov D.Yu. Scattering of sound waves by a finite length elastic cylinder with an inhomogeneous coating // Math. Models&Comput. Simul., 2023, vol. 15, no. 5, pp. 863–876.
Shenderov E.L. Wave Problems of Hydroacoustics. Leningrad: Sudostroenie, 1972. (in Russian)
Nowacki W. Teoria sprezystosci. Warszawa: PWN, 1973.
Brekhovskikh L.M. Waves in Layered Media. Moscow: Nauka, 1973. 344 p. (in Russian)
Ivanov E.A. Diffraction of Electromagnetic Waves on Two Bodies. Minsk: Nauka i Tekhnika, 1968. 584 p. (in Russian)
Timoshenko S.P., Voynovskiy-Kriger S. Plastiny i obolochki. Moscow: Nauka, 1966. 636 p. (in Russian)
Kurant R. Partial Differential Equations. Moscow: Mir, 1964. 830 p. (in Russian)
Shenderov E.L. Radiation and Scattering of Sound. Leningrad: Sudostroenie, 1989. 302 p. (in Russian)
Zav`ialov Yu.S., Kvasov B.I., Miroshnichenko V.L. Spline Function Methods. Moscow: Nauka, 1980. 352 p. (in Russian)
Korobov N.M. Number-Theoretic Methods in Approximate Analysis. Moscow: MTSNMO, 2004. 288 p. (in Russian)
Dobrovol‘skii N.N., Skobel‘tsyn S.A., Tolokonnikov L.A., Larin N.V. About application of number-theoretic grids in problems of acoustics // Chebyshev. sb., 2021, vol. 22, no. 3, pp. 368–382. (in Russian)
Kalitkin N.N. Numerical Methods. Moscow: Fizmatgiz, 1978. 512 p. (in Russian)