Abstract
We consider the inverse problem of determining the covering inhomogeneity of an elastic sphere characterized by the minimal reflection of a plane sound wave in a preset angular sector and frequency range. Based on an analytic solution to the direct problem, a functional expressing the reflection’s intensity is constructed and an algorithm for its minimization is proposed. The analytic expressions describing the mechanical parameters of an inhomogeneous coating are obtained.
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L. A. Tolokonnikov and V. V. Yudachev, “Reflection and refraction of flat sound wave by elastic flat layer with an inhomogeneous coating,” Izv. Tul. Univ., Estestv. Nauki, No. 3, 219–226 (2015).
A. G. Romanov and L. A. Tolokonnikov, “The scattering of acoustic waves by a cylinder with a non-uniform elastic coating,” J. Appl. Math. Mech. 75, 595–600 (2011).
L. A. Tolokonnikov, “Scattering of an incidentally falling plane sound wave by an elastic cylinder with an inhomogeneous coating,” Izv. Tul. Univ., Estestv. Nauki, No. 2, 265–274 (2013).
L. A. Tolokonnikov, “The scattering of a plane sound wave by an elastic sphere with an in-homogeneous coating,” J. Appl. Math. Mech. 78, 367–373 (2014).
L. A. Tolokonnikov, “Diffraction of cylindrical sound waves by an elastic sphere with an in-homogeneous coating,” J. Appl. Math. Mech. 79, 467–474 (2015).
A. O. Vatulyan and P. S. Satunovskii, “On the determination of elastic modules in analysis of fluctuations in an inhomogeneous layer,” Dokl. Phys. 52, 253–255 (2007).
O. V. Bocharova and A. O. Vatulyan, “The reconstruction of density and Youngs modulus of an inhomogeneous rod,” Acoust. Phys. 55, 281–288 (2009).
A. O. Vatulyan, O. V. Yavruyan, and I. V. Bogachev, “Identifying the elastic properties of an inhomogeneous thick layer,” Acoust. Phys. 57, 741–748 (2011).
N. V. Larin, S. A. Skobel’tsyn, and L. A. Tolokonnikov, “Determination of the inhomogeneity laws for an elastic layer with preset sound-reflecting properties,” Acoust. Phys. 61, 504–510 (2015).
N. V. Larin, S. A. Skobeltsyn, and L. A. Tolokonnikov, “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. Univ., Estestv. Nauki, No. 4, 54–62 (2014).
N. V. Larin, S. A. Skobel’tsyn, and L. A. Tolokonnikov, “Modelling the inhomogeneous coating of an elastic plate with optimum sound-reflecting properties,” J. Appl. Math. Mech. 80, 339–344 (2016).
N. N. Lebedev, Special Functions and their Applications (Fizmatgiz, Moscow, Leningrad, 1963) [in Russian].
N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobelkov, Numerical Methods (Binom. Laboratoriia Znanii, Moscow, 2008) [in Russian].
D. Rutkovskaya, M. Pilinskii, and L. Rutkovskii, Neural Networks, Genetic Algorithms and Fuzzy Systems (Goryachaia Liniya Telekom, Moscow, 2006) [in Russian].
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Original Russian Text © L.A. Tolokonnikov, N.V. Larin, S.A. Skobel’tsyn, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 11, pp. 89–98.
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Tolokonnikov, L.A., Larin, N.V. & Skobel’tsyn, S.A. Modeling an Inhomogeneous Coating of an Elastic Sphere with the Required Sound Reflecting Properties. Math Models Comput Simul 10, 333–340 (2018). https://doi.org/10.1134/S2070048218030122
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DOI: https://doi.org/10.1134/S2070048218030122