Determination of the inhomogeneity parameters of an elastic ball anisotropic outer layer by the scattering of a plane sound wave
https://doi.org/10.22405/2226-8383-2022-23-4-350-367
Abstract
The problem of determining the type of inhomogeneity of the external anisotropic layer of an elastic ball from the scattered field of a plane sound wave is considered. It is assumed that the density and elastic moduli of the outer layer material are linear functions of the distance
from the center of the ball. It is believed that the laws of dependency of all moduli of elasticity are identical. According to the acoustic pressure in the vicinity of the ball, it is required to determine the coefficients in the dependences for the density and elastic moduli. The problem of sound diffraction by a ball is solved by a numerical-analytical method. The scattered acoustic field and the field of elastic oscillations in the homogeneous part of the ball is represented by an
expansion in terms of spherical harmonics. For the displacement and stress vector components in an inhomogeneous layer, a boundary value problem is numerically solved based on the equations
of motion and boundary conditions on the layer surfaces. To determine the desired coefficients in the dependences of the density and elastic moduli of the outer layer, the observed pressure
values are compared at a certain set of points on a spherical surface centered at the center of the ball and the calculated pressure values at these points. A variant of forming an indicator of the proximity of observed and calculated pressure values based on the division of observation points into groups is proposed. It is proposed to use the proximity indicator to identify the coefficients in the laws of density inhomogeneity and elastic moduli in the layer.
About the Author
Sergey Alekseevich Skobel’tsyn
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
References
1. D. Colton and A. Kirsch, 1996. “A simple method for solving inverse scattering problems in the
2. resonance region” Inverse Problems vol. 12, pp. 383–393.
3. R. P. Gilbert and Y. Xu, 2000, “Acoustic imaging in a shallow ocean with a thin ice cap” Inverse
4. Problems vol. 16, pp. 1799–1811.
5. B. B.Guzina, S. F. Nintcheu and M. Bonnet, 2003, “On the stress-wave imaging of cavities in
6. a semi-infinite solid” Int. J. Solids Struct., vol. 40, issue 6, pp. 1505–1523.
7. P. A. Martin, 2003, “Acoustic scattering by inhomogeneous obstacles” SIAM J. Appl. Math.,
8. vol. 64, pp. 297–308.
9. E. Bilgin, A. Yapar and T. Yelkenci, 2013, “An acoustic inverse scattering problem for spheres
10. with radially inhomogeneous compressibility” J. Acoust. Soc. Am., V. 133, issue 4, pp. 2097–
11.
12. I. V. Bogachev, R. D. Nedin, A. O. Vatul‘yan and O. V. Yavruyan, 2017, “Identification of
13. inhomogeneous elastic properties of isotropic cylinder” ZAMM - J. Applied Mathematics and
14. Mechanics, vol. 97, issue 3, pp. 358–364.
15. Vatul’yan A. O. and V. O. Yurov, 2020 “On Estimating the Laws of Radial Inhomogeneity in
16. a Cylindrical Waveguide” Acoust. Phys., vol. 66, pp. 97–104.
17. A. O. Vatul’yan, 2022, “On coefficient inverse problems and their applications in mechanics and
18. biomechanics” Mechanics – Proceedings of National Academy of Sciences of Armenia, vol. 75,
19. no. 1, pp. 36–47.
20. N. V. Larin, S. A. Skobel’tsyn and L. A. Tolokonnikov, 2015, “Determination of the
21. inhomogeneity laws for an elastic layer with preset sound-reflecting properties” Acoust. Phys.,
22. vol. 61, issue 5, pp. 504–510.
23. S. A. Skobelt’syn, 2017, “Determination of the parameters of an inhomogeneous coating of an
24. elastic cylinder with a cavity to provide specified sound-reflecting properties” News of TulGU.
25. Technical science, issue 7, pp. 163–175.
26. S. A. Skobelt’syn, 2018, “Determination of the parameters of the inhomogeneity of the coating
27. of an elliptical cylinder by sound scattering in the presence of an elastic half-space” News of
28. TulGU. Technical science, issue 9, pp. 290–302.
29. S. A. Skobelt’syn and N. Y. Peshkov, 2019, “Finding, by means of a scattered sound, the
30. geometric parameters of a finite elastic cylinder located near the half-space border” J. Physics:
31. Conference Series, vol. 1203, 012023, pp. 1–10.
32. S. A. Skobelt’syn and N. Y. Peshkov, 2020, “Determining the thickness of an inhomogeneous
33. coating of a finite elastic cylinder from scattered sound in a half-space” News of TulGU.
34. Technical science, issue 10, pp. 172–183.
35. F. I. Fedorov, 1965, Theory of elastic waves in crystals [Teoriya uprugikh voln v kristallakh],
36. Moscow, Nauka.
37. N. Cherradi, A. Kawasaki and M. Gasik, 1994, “Worldwide trends in functional gradient
38. materials research and development” Composites Engineering, vol. 4, issue 8, pp. 883–894.
39. E. J. Skudryzk, 1971, The Foundations Acoustic, New York, Springer-Verlag.
40. M. A. Isakovich, 1973, General acoustics [Obshchaya akustika], Moscow, Nauka.
41. W. Nowacki, 1963, Dynamics of elastic systems, New York, Wiley.
42. S. A. Skobel’tsyn and L. A. Tolokonnikov, 1995, “Sound scattering by an inhomogeneous
43. transversally isotropic spherical layer” Acoustical Physics, vol. 41, no. 6, pp. 917–923.
44. E. J. Skudryzk, 1971, The Foundations Acoustic, New York, Springer-Verlag.
45. A. N. Guz and etc., 1978, Diffraction of elastic waves [Difraktciya uprugikh voln], Kyiv, Nauk.
46. dumka.
47. G. A. Corn and T. M. Corn, 2000, Mathematical Handbook for Scientists and Engineers, New
48. York, Dover Publications.
49. P. M. Morse and H. Feshbach, 1953, Methods of Mathematical Physics, New York, McGraw-Hill.
50. N. A. Shulga, A. Ya. Grigorenko and T. L. Efimova, 1988, “Free non-axisymmetric vibrations of
51. a thick-walled transversely isotropic hollow sphere”, Appl. Mechanics, vol. 24, no. 5, pp. 12–17.
Review
For citations:
Skobel’tsyn S.A. Determination of the inhomogeneity parameters of an elastic ball anisotropic outer layer by the scattering of a plane sound wave. Chebyshevskii Sbornik. 2022;23(4):350-367. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-350-367
Views:
222
Email this article 