 | | 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
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| In English (Mech. Solids): | | 3212 |
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| S.A. Nazarov, "Asymptotics of the Frequencies of Elastic Waves Trapped by a Small Crack in a Cylindrical Waveguide," Mech. Solids. 45 (6), 856-864 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
6 |
Pages |
856-864 |
| DOI |
10.3103/S0025654410060099 |
| Title |
Asymptotics of the Frequencies of Elastic Waves Trapped by a Small Crack in a Cylindrical Waveguide |
| Author(s) |
S.A. Nazarov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, V.O., St.&nsbp;Petersburg, 199178 Russia, srgnazarov@yahoo.co.uk) |
| Abstract |
An asymptotics of frequencies of waves trapped in a space waveguide with a partially clamped lateral surface and a crack of a small diameter O(h) is obtained. The corresponding eigenvalue is located at a distance O(h6) from the first threshold of the continuous spectrum. |
| Keywords |
elastic waveguide, crack, trapped wave, eigenvalue asymptotics |
| References |
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| 4. | S. A. Nazarov,
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| 9. | S. A. Nazarov,
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| 12. | M. S. Agranovich and M. I. Vishik,
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19 (3), 53-157 (1964)]. |
| 13. | S. A. Nazarov,
"Variational and Asymptotic Methods for Finding Eigenvalues
below the Continuous Spectrum Threshold,"
Sibirsk. Mat. Zh.
51 (5), 1086-1101 (2010)
[Siberian Math. J. (Engl. Transl.)
51 (5), 866-878 (2010)]. |
| 14. | S. A. Nazarov and B. A. Plamenevsky,
Elliptic Problems in Domains with Piecewise Smooth Boundaries
(Nauka, Moscow, 1991; Walter de Gruyter, Berlin, New York, 1994). |
| 15. | I. S. Zorin, A. B. Movchan, and S. A. Nazarov,
"Use of the Elastic Polarisation Tensor in Problems of Crack Mechanics,"
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No. 3, 113-124 (2000)
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| 17. | V. G. Maz'ya and B. A. Plamenevsky,
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| 18. | W. G. Mazja, S. A. Nasarow, and B. A. Plamenewski,
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| 19. | S. A. Nazarov,
"On the 3D Formulation for the Novozhilov Criterion for Quasi-Static Fracture,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 118-127 (2006)
[Mech. Solids (Engl. Transl.)
41 (2), 93-100 (2006)]. |
| 20. | M. Bach, S. A. Nazarov, and W. L. Wendland,
"Stable Propagation on a Model Crack in an Isotropic Elastic Space. Comparison of the Irwin and the Griffith Approaches,"
in Problemi Attuali dell'Analisi e della Fisica Matematica
(Aracne, Rome, 2000),
pp. 167-189. |
|
| Received |
12 August 2010 |
| Link to Fulltext |
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