 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| O. D. Pryakhina and A. V. Smirnova, "On the study of waveguide properties of a stack of elastic layers with a set of rigid inclusions," Mech. Solids. 44 (3), 380-388 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
380-388 |
| DOI |
10.3103/S0025654409030078 |
| Title |
On the study of waveguide properties of a stack of elastic layers with a set of rigid inclusions |
| Author(s) |
O. D. Pryakhina (Kuban State University, Stavropol'skaya 149, Krasnodar, 350040 Russia, donna@kubsu.ru)
A. V. Smirnova (Kuban State University, Stavropol'skaya 149, Krasnodar, 350040 Russia) |
| Abstract |
Although there are quite a few papers dealing with dynamical
processes in semibounded media containing a set of inhomogeneities of various nature, these process are nowadays far from being described completely. Since the stress-strain states of such mechanical systems depend on many parameters, the traditional analytic and numerical methods for their analysis are inefficient even for a small number of imperfections, and some of them cannot be applied at large vibration frequencies and in large domains. In
this connection, it is of interest to study this class of problems in a new setting and develop new numerical-analytic methods for solving these problems. It is especially important to develop methods for studying the resonance properties of mechanical systems.
In the present paper, we consider a set of imperfections of the simplest type, namely, plane rigid inclusions lying in planes parallel to the interfaces in a multilayered semibounded medium. In this case, attention is mainly paid to the analysis of singular sets of the determinants for the symbols of the kernels of systems of integral equations generated by the boundary value problems in the class under study. |
| References |
| 1. | V.A. Babeshko,
"On Calculation of High-Frequency Resonance Parameters in the Three-Dimensional Case,"
Dokl. Ross. Akad. Nauk 335 (1), 55-58 (1994)
[Dokl. Phys. (Engl. Transl.) 39 (3), 186-189 (1994)]. |
| 2. | V.A. Babeshko,
"To the Problem of the Dynamical Fracture of Crack-Type Layered Bodies,"
Dokl. Akad. Nauk SSSR 307 (2), 324-328 (1989). |
| 3. | V.A. Babeshko, O.D. Pryakhina, and A.V. Smirnova,
"Dynamic Problems for Discontinuous Media,"
Prikl. Mekh. 40 (3), 3-10 (2004)
[Int. Appl. Mech. (Engl. Transl.) 40 (3), 241-245 (2004)]. |
| 4. | O.D. Pryakhina and A.V. Smirnova,
"An Analytical Method for Solving Dynamic Problems for Layered Media with Inclusions,"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 87-97 (2005)
[Mech. Solids (Engl. Transl.) 40 (2), 71-79 (2005)]. |
| 5. | O.D. Pryakhina and A.V. Smirnova,
"To the Statement of Dynamical Mixed Problems for Layered Media with Imperfections,"
Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz Region. Estestv. Nauki, No. 2, 29-31 (2003). |
| 6. | O.D. Pryakhina and A.V. Smirnova,
"An Efficient Method of Solving Dynamic Problems for Layered Media with Discontinuous Boundary Conditions,"
Prikl. Mat. Mekh. 68 (3), 499-506 (2004)
[J. Appl. Math. Mech. (Engl. Transl.) 68. (3), 447-453 (2004)]. |
| 7. | O.D. Pryakhina, A.V. Smirnova, D.V. Borisov, and V.A. Mazin,
"Properties of Elements and Determinants of the Matrix-Symbols of Dynamical Problems for Multilayered Media with Inclusions,"
Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz Region. Estestv. Nauki, No. 2, 40-43 (2005). |
| 8. | I.I. Vorovich, V.A. Babeshko, and O.D. Pryakhina,
Dynamics of Massive Bodies and Resonance Phenomena in Deformable Media (Nauch. Mir, Moscow, 1999) [in Russian]. |
| 9. | V.A. Babeshko,
"Dynamics of Media with a Set of Inhomogeneities or Imperfections and the Theory of Vibration Strength Viruses,"
Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz Region. Estestv. Nauki, No. 1, 24-26 (1998). |
| 10. | V.A. Babeshko,
"Media with Inhomogeneities (the Case of Inclusions Combined with Cracks)"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 5-9 (2000)
[Mech. Solids (Engl. Transl.) 35 (3), 3-7 (2000)]. |
| 11. | V.A. Babeshko,
"Theory of Vibration Strength Viruses for a Set of Inclusions,"
Izv. Vyssh. Uchebn. Zaved. Sev.-Kavkaz Region. Estestv. Nauki, No. 3, 21-23 (2000). |
| 12. | V.A. Babeshko and O.M. Babeshko,
"Factorization Method for Boundary Value Problems in Unbounded Domains,"
Dokl. Ross. Akad. Nauk 392 (6), 767-770 (2003)
[Dokl. Phys. (Engl. Transl.) 48 (10), 594-597 (2003)]. |
| 13. | V.A. Babeshko and O.M. Babeshko,
"Factorization Method in the Theory of Vibration-Strength Viruses,"
Dokl. Ross. Akad. Nauk 393 (4), 473-477 (2003)
[Dokl. Phys. (Engl. Transl.) 48 (12), 669-673 (2003)]. |
| 14. | V.A. Babeshko and O.M. Babeshko,
"Generalized Factorization in Boundary Value Problems in Multiply Connected Domains,"
Dokl. Ross. Akad. Nauk 392 (2), 185-189 (2003)
[Dokl. Phys. (Engl. Transl.) 48 (9), 512-516 (2003)]. |
|
| Received |
12 April 2006 |
| Link to Fulltext |
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