Modeling the inhomogeneous anisotropic coating of an elastic cylinder that provides minimal sound reflection
https://doi.org/10.22405/2226-8383-2022-23-1-293-311
Abstract
The article deals with the mathematical modeling of an inhomogeneous anisotropic coating of the elastic cylinder, providing the least reflection upon diffraction of a harmonic cylindrical sound wave. It is assumed that the elastic cylinder is homogeneous and isotropic, the coating material is radially inhomogeneous and transversely isotropic, the laws inhomogeneities of the
coating material are described by continuous functions, the body is placed in a boundless ideal fluid.
An analytical solution of the direct diffraction problem is obtained. The scattered acoustic field and wave fields in the cylinder and its coating are defined.
Wave fields in a containing medium and a homogeneous isotropic cylinder are described by expansions in cylindrical 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.
An analytical solution of the inverse problem of the diffraction about the determination of the inhomogeneity laws of the coating material, ensuring the minimum sound scattering in the specified frequency range at a fixed angle of observation and also at a given observation sector at a fixed frequency is obtained. The functionals expressing the average intensity of sound scattering in given frequency range and angular sector of observation are built. Minimization
of the functionals are implemented with the help of the burnout simulation algorithm.
The results of numerical calculations of frequency and angular dependencies of the intensity of the scatter acoustic field in the far zone at the optimal parabolic inhomogeneity laws are presented.
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
Dmitrii Yurevich Efimov
Tula State University
Russian Federation
Russian Federation
postgraduate student
References
1. Honarvar, F. & Sinclair, A. 1997, “Scattering of an obliquely incident plane wave from a circular clad rod”, J. Acoust. Soc. Am., vol. 102, no. 1, pp. 41—48.
2. Fathi-Haftshejani, P. & Honarvar, F. 2019, “Nondestructive evaluation of clad rods by inversion of acoustic scattering data”, J. of Nondestructive Evaluation, vol. 38, no. 3 (67), pp. 1–9.
3. Kosarev, O. I. 2012, “Diffraction of sound by an elastic cylindrical shell with a coating”, Probl. Mashinostr. Nadezh. Mashin, vol. 46, no 1, pp. 34–37, [in Russian].
4. Hasheminejad, S. M. & Safari, N. 2005, “Acoustic scattering from viscoelastically coated spheres and cylinders in viscous fluids”, J. of Sound and Vibration, vol. 280, no. 1, pp. 101–125.
5. Ivanov, V.P. 2006, “Analysis of the field diffracted by a cylinder with a perforated coating”, Acoustical Physics vol. 52, no 6, pp. 683–690.
6. Bobrovnitskii, Yu. I. 2008, “A nonscattering coating for a cylinder”, Acoustical Physics, vol. 54, no 6, pp. 758–768.
7. Bobrovnitskii, Yu. I., Morozov, K. D. & Tomilina, T. M. 2010, “A periodic surface structure with extreme acoustic properties”, Acoustical Physics, vol. 56, no 2, pp. 127–131.
8. Romanov, A. G. & Tolokonnikov, L. A. 2011, “The scattering of acoustic waves by a cylinder with a non-uniform elastic coating”, J. Appl. Math. Mech., vol. 75, no. 5, pp. 595–600.
9. Tolokonnikov, L. A. 2013, “Diffraction of cylindrical sound waves by an cylinder with a nonuniform elastic coating”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 3, pp. 202–208, [in Russian].
10. Tolokonnikov, L. A. 2013, “Scattering of an obliquely incident plane sound wave by an elastic cylinder with a non-uniform covering”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 2-2, pp. 265–274, [in Russian].
11. Larin, N. V. & Tolokonnikov, L. A. 2015, “The scattering of a plane sound wave by an elastic cylinder with a discrete-layered covering”, J. Appl. Math. Mech., vol. 79. no 2, pp. 164–169.
12. Tolokonnikov, L. A. & Efimov, D.Yu. 2021, “ Diffraction of cylindrical sound waves by an elastic cylinder with radially inhomogeneous coating Chebyshevskii sbornik, vol. 22, no. 1, pp. 460–472, [in Russian].
13. Tolokonnikov, L. A. 2018, “Diffraction of a spherical sound wave by an elastic cylinder with an non-uniform coating Chebyshevskii sbornik, vol. 19, no. 4, pp. 215—226, [in Russian].
14. Larin, N. V. 2017, “Diffraction of a plane acoustic wave on the thermoelastic cylinder with the continuously inhomogeneous covering”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no 6, pp. 154–173, [in Russian].
15. Larin, N. V. 2017, “Influence of the continuously inhomogeneous coating on the thermoelastic cylinder sound-reflecting properties”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 9-1, pp. 395–403, [in Russian].
16. Tolokonnikov, L. A., Larin, N. V. & Skobel’tsyn, S. A. 2014, “About definition of linear laws of heterogeneity of the cylindrical elastic layer having the least reflexion in the set direction at sound scattering”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 4, pp. 54–62, [in Russian].
17. Tolokonnikov, L. A., Larin, N. V. & Skobel’tsyn, S. A. 2017, “Modeling of inhomogeneous coating of an elastic cylinder with given sound-reflecting properties”, J. Appl. Mech. and Techn. Physics, no. 4, pp. 733–742.
18. Tolokonnikov, L. A. 2017, “Determination of the inhomogeneity laws for an covering of an elastic cylinder with cylindrical cavity,providing minimum sound reflexion”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki , no 4, pp. 67–81, [in Russian].
19. Tolokonnikov, L. A. 2018, “Diffraction of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surface”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 9, pp. 276–289, [in Russian].
20. Tolokonnikov, L. A., Larin, N. V. 2020, “About influence of an inhomogeneous coating of an elastic cylinder on sound scattering in the presense of a flat surface ”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki , no. 9, pp. 111–118, [in Russian].
21. Tolokonnikov, L. A. & Efimov, D.Yu. 2021, “Diffraction of Sound Waves at an Elastic Cylinder with an Inhomogeneous Coating in the Vicinity of the Boundary of an Elastic Half-Space”, Mechanics of Solids, vol. 56, no. 8, pp. 1641–1648.
22. Tolokonnikov, L. A. 2015, “Diffraction of sound waves by an elastic cylinder with an non-uniform coating in a plane waveguide with acoustic soft boundaries”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 1, pp. 43–53, [in Russian].
23. Tolokonnikov, L. A. 2015, “Diffraction of sound waves by an elastic cylinder with an non-uniform coating in a plane waveguide with absolutely rigid boundaries”, Izv. Tul. Gos. Univ., Ser. Estestv. Nauki, no. 2, pp. 76–83, [in Russian].
24. Tolokonnikov, L. A. 2019, “Scattering of sound waves by an cylinder with an radial non-uniform elastic coating in a planar waveguide”, Chebyshevskii sbornik, vol. 20, no. 1, pp. 270–281, [in Russian].
25. Tolokonnikov, L. A., Larin, N. V. 2021, “Scattering by a cylinder with a inhomogeneous coating of sound waves radiated linear source in a flat waveguide ”, Mathematical modelling, vol. 33, no. 8, pp. 97–113, [in Russian].
26. Tolokonnikov, L. A. & Larin, N. V. 2018, “Mathematical modelling of an inhomogeneous coating of an elastic coating in a plane waveguide”, Izv. Tul. Gos. Univ., Ser. Tekh. Nauki, no. 9, pp. 315–323, [in Russian].
27. Tolokonnikov, L. A. & Belkin A. E. 2020, “Determination of the inhomogeneity laws of a cylinder covering located in a plane waveguide for providing minimum sound reflection”, Chebyshevskii
28. sbornik, vol. 21, no. 4, pp. 354–368, [in Russian].
29. Shenderov, E. L. 1972, “Wave problems of underwater acoustics”, Sudostroenie, Leningrad, 352 p. [in Russian].
30. Ivanov, E. A. 1968, “Diffraction of electromagnetic waves by two bodies”, Nauka i tekhnika, Minsk, 584 p., [in Russian].
31. Nowacki, W.1973, “Teoria sprezystosci”, PWN, Warszawa.
32. Fedorov, F.˙I. 1965, “Theory of elastic waves in crystals”, Nauka, Moscow, 388 p., [in Russian].
33. Lebedev, N. N. 1963, “Special Functions and their Applications”, Fizmatgiz, Moscow, 358 p., [in Russian].
34. Lopatin, A. S. 2005, “Annealing method”, Stochastic optimization in computer science, SPtb. Gos. Univ., no. 1, pp. 133–149, [in Russian].
35. Zavyialov, Yu. S., Kvasov, B. I. & Miroshnichenko, V. L. 1980, “Spline function methods”, Nauka, Мoscow, 352 p.,[in Russian].
Review
For citations:
Tolokonnikov L.A., Efimov D.Yu. Modeling the inhomogeneous anisotropic coating of an elastic cylinder that provides minimal sound reflection. Chebyshevskii Sbornik. 2022;23(1):293-311. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-1-293-311
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