 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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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 |
| Link to Fulltext |
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