Diffraction of a plane sound wave by an elastic sphere with an inhomogeneous transversal isotropic layer
https://doi.org/10.22405/2226-8383-2021-22-4-332-343
Abstract
isotropic elastic sphere with a continuously inhomogeneous anisotropic elastic layer is considered.
It is believed that the body is placed in an infinite ideal fluid, the laws of heterogeneity of the coating material are described by continuous functions.
An analytical solution to the diffraction problem is obtained for the case when the material of the sphere layer is radially inhomogeneous and transversally isotropic.
Wave field in a containing medium and a homogeneous isotropic sphere are described by expansions in spherical wave functions. A boundary value problem is constructed for a system of ordinary differential equations of the second order for finding displacement fields in an inhomogeneous anisotropic layer of sphere.
The results of numerical calculations of directional patterns for scattered acoustic field in the far zone are presented. It is shown that anisotropy of continuously inhomogeneous elastic layer one can substantially change the scattering characteristics of spherical bodies.
About the Authors
Lev Alekseevich Tolokonnikov
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Sergey Lvovich Tolokonnikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Faran, J. J. 1951, “Sound scattering by solid cylinders and spheres”, J. Acoust. Soc. Amer., vol. 23, no. 4, pp. 405 – 418.
2. Junger, M. C. 1952, “Sound scattering by thin elastic shells”, J. Acoust. Soc. Amer., vol. 24, no. 4, pp. 366 – 373.
3. Flax, L., Dragonette, L. R. & Uberall, H. 1978, “Theory of elastic resonance excitation by sound scattering”, J. Acoust. Soc. Amer., vol. 63, no. 3, pp. 723 – 731.
4. Goodman, R. D. & Stern, R. 1962, “Reflection and transmission of sound by elastic spherical shells”, J. Acoust. Soc. Amer., vol. 34, no 3, pp. 338 – 344.
5. Prikhod’ko, V.Yu. & Tyutekin, V. V. 1987, “Eigenfrequencies and normal modes of a radially layered elastic body, Soviet Applied Mechanics, vol. 23, no 6, pp. 518 – 522.
6. Shenderov, E. L. 1989, “Radiation and scattering of sound”, Sudostroenie, Leningrad, 304 p., [in Russian].
7. Skobel’tsyn, S. A. & Tolokonnikov, L. A. 1995, “Sound scattering by an inhomogeneous transversaly isotropic spherical layer”, Acoustical Physics, vol. 41, no 6, pp. 812 – 818.
8. Larin, N. V. & Tolokonnikov, L. A. 2010, “Scattering of sound by an inhomogeneous thermoelastic spherical layer”, J. Appl. Math. Mech., vol. 74, no. 4, pp. 460 – 466.
9. Brigodirova, T.E˙ . & Medvedskii A.L˙ . 2007, “Diffraction of a nonstationary acoustic wave by an inhomogeneous transversely isotropic hollow sphere”, J. Mechanics of Composite Materials and Structures, vol. 13, no. 1, pp. 119 – 130, [in Russian].
10. Tolokonnikov, L. A. 2014, “The scattering of a plane sound wave by an elastic sphere with an inhomogeneous coating”, J. Appl. Math. Mech., vol. 78, no. 4, pp. 367 – 373.
11. Tolokonnikov, L.A. & Rodionova, G.A. 2014, “Diffraction of a spherical acoustic wave by an elastic sphere with a non-uniform covering”,Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 3, pp.
12. – 137, [in Russian].
13. Tolokonnikov, L. A. 2015, “Diffraction of cylindrical sound waves by an elastic sphere with an inhomogeneous coating”, J. Appl. Math. Mech., vol. 79, no. 5, pp. 467 – 474.
14. Tolokonnikov, L. A. 2014, “Diffraction of a plane acoustic wave by an elastic sphere with a nonuniform covering and arbitrarily situated spherical vacuity”,Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 2, pp. 181 – 193, [in Russian].
15. Tolokonnikov, L. A., Larin, N. V. & Skobel’tsyn,S. A. 2018, “Modeling an inhomogeneous coating of an elastic sphere with the required sound reflecting properties”, Mathematical Models and Computer Simulations, vol. 10, no. 3, pp. 333 – 340.
16. Larin, N.V. & Tolokonnikov. L. A. 2019, “Sound Scattering by a Thermoelastic Ball with a Continuously Inhomogeneous Coating in a Heat-Conducting Fluid”, Mathematical Models and
17. Computer Simulations, vol. 11, no. 6, pp. 1007 – 1018.
18. Tolokonnikov, L. A. 2017, “Modelling of a continuously inhomogeneous coating of an elastic sphere by a system of homogeneous elastic layers in the problem of sound scattering”, J. Appl. Math. Mech., vol. 81, no. 6, pp. 480 – 485.
19. Shenderov, E. L. 1972, “Wave problems of underwater acoustics”, Sudostroenie, Leningrad, 352 p. [in Russian].
20. Nowacki, W.1973, “Teoria sprezystosci”, PWN, Warszawa.
21. Ivanov, E. A. 1968, “Diffraction of electromagnetic waves by two bodies”, Nauka i tekhnika, Minsk, 584 p., [in Russian].
22. Lebedev, N. N. 1963, “Special Functions and their Applications”, Fizmatgiz, Moscow, 358 p., [in Russian].
Review
For citations:
Tolokonnikov L.A., Tolokonnikov S.L. Diffraction of a plane sound wave by an elastic sphere with an inhomogeneous transversal isotropic layer. Chebyshevskii Sbornik. 2021;22(4):332-343. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-4-332-343
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