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IssuesArchive of Issues2005-2pp.71-79

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Total articles in the database: 9179
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O. D. Pryakhina and A. V. Smirnova, "An analytical method for solving dynamic problems for layered media with inclusions," Mech. Solids. 40 (2), 71-79 (2005)
Year 2005 Volume 40 Number 2 Pages 71-79
Title An analytical method for solving dynamic problems for layered media with inclusions
Author(s) O. D. Pryakhina (Krasnodar)
A. V. Smirnova (Krasnodar)
Abstract An efficient analytical method is proposed for the solution of dynamic problems for layered media containing inclusion-type defects at the interfaces between the layers. New matrix function formulas and systems of integral equations which relate the displacements and the stress jumps on the inclusion boundaries are derived. For some specific media, a number of examples of using the relations obtained is given and the numerical analysis is performed.

A method of constructing the solution of dynamic problems for layered media in the presence of crack-type defects was proposed in [1, 2]. Other approaches to the solution of the problems of this kind were presented in [3-9]. The conditions for the localization of vibration processes due to a system of cracks and/or inclusions were established in [5-6].

The investigation of the issues under consideration is motivated by their practical importance in the field of seismology, seismography, defectoscopy, electronics, etc.
1.  O. D. Pryakhina and A. V. Smirnova, "An efficient method for solving dynamic problems for layered media with discontinuous boundary conditions," PMM [Applied Mathematics and Mechanics], Vol. 68, No. 3, pp. 500-507, 2004.
2.  O. D. Pryakhina and A. V. Smirnova, "On the formulation of mixed dynamic problems for layered media with defects," Izv. Vuzov. Sev.-Kavkaz. Region. Estestv. Nauki, No. 2, pp. 29-31, 2003.
3.  V. M. Alexandrov, B. I. Smetanin, and B. V. Sobol', Thin Stress Concentrators in Elastic Bodies [in Russian], Nauka, Moscow, 1993.
4.  V. M. Alexandrov and D. A. Pozharskii, "To the problem of a crack on the elastic strip-half-plane interface," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 86-93, 2001.
5.  V. A. Babeshko, "Media with inhomogeneities (the case of inclusions combined with cracks)," Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 5-9, 2000.
6.  V. A. Babeshko, "On the problem of dynamic fracture of fissured layered bodies," Doklady AN SSSR, Vol. 207, No. 2, pp. 324-327, 1989.
7.  V. A. Babeshko, A. V. Pavlova, S. V. Ratner, and R. T. Williams, "On the solution to the problem of vibration of an elastic body containing a system of internal cavities," Doklady AN, Vol. 382, No. 5, pp. 625-628, 2002.
8.  E. V. Glushkov, N. V. Glushkova, and A. V. Ekhlakov, "A mathematical model of an ultrasonic defectoscopy of spatial cracks," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 1, pp. 147-156, 2002.
9.  G. S. Kit, V. V. Mikhaskiv, and O. M. Khai, "The analysis of steady oscillations of a plane rigid inclusion in a 3D elastic body using the boundary element method," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 5, pp. 855-863, 2002.
10.  V. A. Babeshko, The Generalized Factorization Method in Spatial Mixed Dynamic Problems of Elasticity [in Russian], Nauka, Moscow, 1984.
11.  I. I. Vorovich, V. A. Babeshko, and O. D. Pryakhina, Dynamics of Massive Bodies and Resonant Phenomena in Deformable Media [in Russian], Nauchnyi Mir, Moscow, 1999.
12.  V. M. Seimov, A. N. Trofimchuk, and O. A. Savitskii, Vibrations and Waves in Layered Media [in Russian], Naukova Dumka, Kiev, 1990.
13.  V. A. Babeshko, E. V. Glushkov, and Zh. F. Zinchenko, Dynamics of Inhomogeneous Linear Elastic Media [in Russian], Nauka, Moscow, 1989.
Received 22 June 2004
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