 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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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. |
| References |
| 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 |
| << Previous article | Volume 40, Issue 2 / 2005 | Next article >> |
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