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IssuesArchive of Issues2018-1pp.33-44

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E.V. Rozhkova, "To the Investigation of Plane Wave Propagation in an Elastic Anisotropic Media by a Recursive Operator Method," Mech. Solids. 53 (1), 33-44 (2018)
Year 2018 Volume 53 Number 1 Pages 33-44
DOI 10.3103/S0025654418010041
Title To the Investigation of Plane Wave Propagation in an Elastic Anisotropic Media by a Recursive Operator Method
Author(s) E.V. Rozhkova (Tashkent Institute of Railway Transport Engineers, ul. Chambil 1, Tashkent, Uzbekistan, rojkova-elena@mail.ru)
Abstract A solution of the equations of motion of a 3D anisotropic elastic medium without determining the roots of the determinant (secular) equation is obtained by a recursive operator method. A relationship between such solutions and classical solutions is established. The possibility of solving initial-boundary value problems for plane waves is considered. An example and comparative graphs of the solutions are given.
Keywords recursive operator method, determinant equation, matrix of constant coefficients, factorial power
References
1.  F. I. Fedorov, The Theory of Elastic Waves in Crystals (Nauka, Moscow, 1965) [in Russian].
2.  G. I. Petrashen', Propagation of Waves in Elastic Anisotropic Media (Nauka, Leningrad, 1980) [in Russian].
3.  V. N. Frolov, Special Classes of Functions in the Anisotropic Theory of Elasticity (Fan, Tashkent, 1981) [in Russian].
4.  Yu. L. Spivakov, Special Classes of Solutions of Linear Differential Equations and Their Applications to the Anisotropic and Inhomogeneous Theory of Elasticity (Fan, Tashkent, 1986) [in Russian].
5.  E. V. Rozhkova, "Solutions of the Complete System of Equations of the Theory of Elasticity in Stresses by the Recursive Operator Method," Dokl. AN Resp. Uzbekistan, No. 3-4, 59-66 (2009).
6.  E. V. Rozhkova, "Solution of Systems of Recursive Equations by Reducing to a Solution of One Recursive Equation," Uzb. Mat. Zh., No. 2, 108-120 (2011).
7.  E. V. Rozhkova and Yu. L. Spivakov, "Solution of the System of Equations of a Viscoelastic Medium Motion by Splitting it into Two Noncommuting Operators," Uzb. Mat. Zh., No. 3, 74-80 (2007).
8.  L. A. Ryabinkin, Theory of elastic waves (Nedra, Moscow, 1987) [in Russian].
9.  E. V. Rozhkova, "To the solution of the Lamb problem for an elastic anisotropic half-space by the recursive operator method," in Problems of Seismology in Uzbekistan, No. 5 (2008), pp. 219-222 .
10.  E. V. Rozhkova, "Operator algorithm for determining the fields of waves excited by point sources in anisotropic elastic media," Vopr. Vych. Prikl. Mat., No. 112, 74-82 (2003).
Received 24 April 2015
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