Diffraction of a spherical sound wave by an elastic cylinder with an non-uniform anisotropic coating
https://doi.org/10.22405/2226-8383-2022-23-4-368-381
Abstract
In paper the problem of the diffraction of a spherical monochromatic sound wave on a homogeneous isotropic elastic cylinder with a radially non-uniform anisotropic elastic coating.
It is assumed that the body is located in a free space filled with an ideal liquid. The analytical solution of the problem is obtained.
In the case of steady-state oscillations, the propagation of small perturbations in an ideal fluid is described by the Helmholtz scalar equation. The radiation field of a spherical source is written as a series expansion in cylindrical wave functions. The propagation of elastic waves in an isotropic elastic cylinder is described by the scalar and vector Helmholtz equations. The oscillations of an non-uniform anisotropic elastic cylindrical layer are described by the general
equations of motion of a continuous medium.
The asymptotic formula for the far field zone is obtained by the steepest descent method.
Numerical calculations of the frequency characteristics of the scattered field are carried out for elastic cylinders with homogeneous and inhomogeneous transversally isotropic coatings, as well as for the case of a homogeneous isotropic coating. A significant influence and mutual influence of the inhomogeneity and anisotropy of the coating material on the acoustic properties of the scattering cylindrical body is revealed.
About the Authors
Lev Alexeevich Tolokonnikov
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Dmitrii Yurevich Efimov
Tula State University
Russian Federation
Russian Federation
postgraduate student
References
1. Ivanov, V.P. 2006, “Analysis of the field diffracted by a cylinder with a perforated coating”,
2. Acoustical Physics vol. 52, no 6, pp. 683-690.
3. Bobrovnitskii, Yu. I. 2008, “A nonscattering coating for a cylinder”, Acoustical Physics, vol. 54,
4. no 6, pp. 758-768.
5. Kosarev, O. I. 2012, “Diffraction of sound by an elastic cylindrical shell with a coating”, Probl.
6. Mashinostr. Nadezh. Mashin, vol. 46, no 1, pp. 34-37, [in Russian].
7. Romanov, A. G. & Tolokonnikov, L. A. 2011, “The scattering of acoustic waves by a cylinder
8. with a non-uniform elastic coating”, J. Appl. Math. Mech., vol. 75, no. 5, pp. 595-600.
9. Tolokonnikov, L. A. 2013, “Scattering of an obliquely incident plane sound wave by an elastic
10. cylinder with a non-uniform covering”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 2-2,
11. pp. 265-274, [in Russian].
12. Larin, N. V. & Tolokonnikov, L. A. 2015, “The scattering of a plane sound wave by an elastic
13. cylinder with a discrete-layered covering”, J. Appl. Math. Mech., vol. 79. no 2, pp. 164-169.
14. Tolokonnikov, L. A., Larin, N. V. & Skobel’tsyn, S. A. 2017, “Modeling of inhomogeneous coating
15. of an elastic cylinder with given sound-reflecting properties”, J. Appl. Mech. and Techn. Physics,
16. no. 4, pp. 733-742.
17. Tolokonnikov, L. A. 2013, “Diffraction of cylindrical sound waves by an cylinder with a nonuniform
18. elastic coating”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 3, pp. 202-208, [in
19. Russian].
20. Tolokonnikov, L. A. & Efimov, D.Yu. 2021, “ Diffraction of cylindrical sound waves by an elastic
21. cylinder with radially inhomogeneous coating Chebyshevskii sbornik, vol. 22, no. 1, pp. 460-472,
22. [in Russian].
23. Tolokonnikov, L. A. 2018, “Diffraction of a spherical sound wave by an elastic cylinder with an
24. non-uniform coating Chebyshevskii sbornik, vol. 19, no. 4, pp. 215–226, [in Russian].
25. Skobel’tsyn, S. A. & Tolokonnikov, L. A. 1995, “Scattering of sound waves by a transversely
26. isotropic inhomogeneous cylinder layer”, Acoustical Physics, vol. 41, no 1, pp. 114-117.
27. Tolokonnikov L. A. 1998, “Difraktciia tcilindricheskikh voln na neodnorodnoi transversalnoizotropnoi
28. tcilindricheskoi obolochke”, Oboronnaia tekhnika, no. 4–5. pp. 9–11, [in Russian].
29. Larin, N. V. & Belkin, A. E. 2021, “Sound scattering on a solid cylinder with an elastic
30. anisotropic inhomogeneous coating ”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 11, pp. 107-117,
31. [in Russian].
32. Skobel’tsyn, S. A. 2021, “Diffraction problem of plane sound wave by elastic cylinder with
33. transversely-isotropic inhomogeneous coating”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 11,
34. pp. 230-239, [in Russian].
35. Tolokonnikov, L. A. & Efimov D.Yu. 2022, “Modeling the inhomogeneous anisotropic coating
36. of an elastic cylinder that provides minimal sound reflection”, Chebyshevskii sbornik, vol. 23,
37. no. 1, pp. 293–311, [in Russian].
38. Shenderov, E. L. 1972, “Wave problems of underwater acoustics”, Sudostroenie, Leningrad,
39. p. [in Russian].
40. Ivanov, E. A. 1968, “Diffraction of electromagnetic waves by two bodies”, Nauka i tekhnika,
41. Minsk, 584 p., [in Russian].
42. Nowacki, W. 1973, “Teoria sprezystosci”, PWN, Warszawa.
43. Fedorov, F. I. 1965, “Theory of elastic waves in crystals”, Nauka, Moscow, 388 p., [in Russian].
44. Ilyin, A. M. & Danilin, A. R. 2009, “Asymptotic Methods in Analysis”, Fizmatlit, Moscow, 248
45. p, [in Russian].
46. Lebedev, N. N. 1963, “Special Functions and their Applications”, Fizmatgiz, Moscow, 358 p., [in
47. Russian].
48. Bhatnagar, P. L. 1979, Nonlinear Waves in One-dimensional Dispersive Systems, Oxford
49. University Press, 142 p.
50. Zavyialov, Yu. S., Kvasov, B. I. & Miroshnichenko, V. L. 1980, “Spline function methods”, Nauka,
51. Мoscow, 352 p., [in Russian].
52. Samarskii, A. A. & Gulin, A. V. 1989, “Numerical methods“, Moscow, Nauka, 432 p., [in Russian].
Review
For citations:
Tolokonnikov L.A., Efimov D.Yu. Diffraction of a spherical sound wave by an elastic cylinder with an non-uniform anisotropic coating. Chebyshevskii Sbornik. 2022;23(4):368-381. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-368-381
Views:
231
Email this article 