Reflection and transmission of cylindrical sound wave through an elastic plate with an inhomogeneous coating
https://doi.org/10.22405/2226-8383-2022-23-5-305-319
Abstract
In paper the problem of spherical sound wave reflection and transmission through a homogeneous isotropic elastic plate with a continuously inhomogeneous in thickness elastic coating is considered. It is believed that the plate is placed in an infinite ideal fluid, and the incident sound wave is harmonic and is generated by point source.
An analytical solution of the posed problem is obtained on the basis of the known solution of the problem about the passage of plane sound waves through plate with a continuously inhomogeneous coating and using integral representation of a spherical wave in the form of an expansion on flat waves.
Finding the displacement field in an inhomogeneous layer is reduced to solving boundary value problem for a system of ordinary differential equations of the second order.
The results of numerical calculations of frequency characteristics are presented for reflected and transmitted acoustic fields.
Keywords
reflection and transmission of sound,
spherical sound wave,
homogeneous elastic plate,
inhomogeneous coating.
Supporting agencies: Supported by the Russian Science Foundation grant No. 18-11-00199, https://rscf.ru/project/18-11-00199/
About the Authors
Lev Alexeevich Tolokonnikov
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Thi Sang Nguyen
Tula State University
Russian Federation
Russian Federation
postgraduate student
References
1. Tolokonnikov, L.A. & Yudachev, V. V. 2015, “Reflection and refraction of a planar acoustic
2. waves in an elastic planar layer with a non-uniform covering”, Izv. Tul. Gos. Univ., Ser. Estestv.
3. Nauki, no. 3, pp. 219 – 226, [in Russian].
4. Larin, N. V., Skobel’tsyn, S. A. & Tolokonnikov, L. A. 2016, “Modeling the inhomogeneous
5. coating of an elastic plate with optimum sound-reflecting properties”, J. Appl. Math. Mech.,
6. vol. 80, no. 4, pp. 339 – 344.
7. Larin, N. V. 2016, “Determination of the inhomogeneity laws for coating of the thermoelastic
8. plate to obtain minimum sound reflection”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 11-2,
9. pp. 216 – 234, [in Russian].
10. Tolokonnikov, L. A. & Nguyen, T. S. 2018, “About the influence of an non-uniform covering of
11. the elastic plate on sound reflection and transmission”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki,
12. no. 6, pp. 362 – 372, [in Russian].
13. Tolokonnikov, L. A. & Nguyen, T. S. 2019, "The transmission of sound through an elastic plate
14. with an inhomogeneous coating adjoining viscous liquids Chebyshevskii sbornik, vol. 20, no. 2,
15. pp. 311 -– 324, [in Russian].
16. Nguyen, T. S. 2021, “About reflection and transmission of a plane sound wave through an elastic
17. plate with an inhomogeneous coating adjoining viscous liquids”, Izv. Tul. Gos. Univ., Ser. Tekh.
18. Nauki, no. 5, pp. 404 – 414, [in Russian].
19. Skobel’tsyn, S. A. 2017, “Tstimation of the coating properties of a finite plate with a cavity
20. providing the given parameters of the sound reflection”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki,
21. no. 7, pp. 83 – 92, [in Russian].
22. Tolokonnikov, L. A. & Tolokonnikov, L. A. 2021, "Reflection and reflaction of a plane sound
23. wave in an elastic plate with an inhomogeneous anisotropic coating Chebyshevskii sbornik, vol.
24. , no. 3, pp. 423 – 437, [in Russian].
25. Tolokonnikov, L. A. & Nguyen, T. S. 2022, "Reflection and transmission of cylindrical sound
26. wave through an elastic plate with an inhomogeneous coating Chebyshevskii sbornik, vol. 23,
27. no. 1, pp. 312 -– 327, [in Russian].
28. Piquette J. C. 1988, "Spherical-wave scattering by a finite-thickness solid plate of infinite lateral
29. extent, with some implications for panel measurements J. Acoust. Soc. Am., vol. 83, No. 4, pp.
30. – 1294.
31. Shushkevich G. Ch. & Kiselyova N. N. 2014, "Sound field shielding by flat elastic layer and thin
32. unclosed spherical shell”, Informatika, no. 2, pp. 36 – 47, [in Russian].
33. Shenderov, E. L. 1972, “Wave problems of underwater acoustics”, Sudostroenie, Leningrad,
34. p., [in Russian].
35. Nowacki, W.1973, “Teoria sprezystosci”, PWN, Warszawa.
36. Brekhovskikh, L. M. 1973, “Waves in Layered Media”, Nauka, Moscow, 344 p., [in Russian].
37. Tolokonnikov, L. A. & Nguyen, T. S. 2020, "Determination of the displacement field in
38. an inhomogeneous coating of an elastic plate when passing through her plane sound
39. wave Chebyshevskii sbornik, vol. 21, no. 1, pp. 310 -– 321, [in Russian].
Review
For citations:
Tolokonnikov L.A., Nguyen T.S. Reflection and transmission of cylindrical sound wave through an elastic plate with an inhomogeneous coating. Chebyshevskii Sbornik. 2022;23(5):305-319. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-5-305-319
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