 | | 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: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| Nazarov S.A., "Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies," Mech. Solids. 55 (8), 1328-1339 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
8 |
Pages |
1328-1339 |
| DOI |
10.3103/S002565442008018X |
| Title |
Waves Trapped by Semi-Infinite Kirchhoff Plate at Ultra-Low Frequencies |
| Author(s) |
Nazarov S.A. (St. Petersburg State University, St. Petersburg, 199034 Russia, srgnazarov@yahoo.co.uk) |
| Abstract |
In this paper, a semi-infinite Kirchhoff plate with a traction-free edge, which rests partially on a heterogeneous Winkler foundation (the Neumann problem for the biharmonic operator perturbed by a small free term with a compact support), is considered. It is shown that, for arbitrary small ε>0, a variable foundation compliance coefficient (defined nonuniquely) of order ε can be constructed, such that the plate obtains the eigenvalue ε4 that is embedded into a continuous spectrum, and the corresponding eigenfunction decays exponentially at infinity. It is verified that no more than one small eigenvalue can exist. It is noteworthy that a small perturbation cannot prompt an emergence of an eigenvalue near the cutoff point of the continuous spectrum in an acoustic waveguide (the Neumann problem for the Laplace operator). |
| Keywords |
semi-infinite Kirchhoff plate, Winkler foundation, small perturbation, threshold resonance, near-threshold eigenvalue embedded into continuous spectrum |
| Received |
06 August 2019 | Revised |
16 March 2020 | Accepted |
02 April 2020 |
| Link to Fulltext |
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