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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 10, Pages 1713–1726 (Mi zvmmf10285)  

Eigenmodes of a thin elastic layer between periodic rigid profiles

S. A. Nazarovabc

a St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504, Russia
b St. Petersburg State Polytechnical University, Politekhnicheskaya ul. 29, St. Petersburg, 195251, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoi pr. 61, V.O., St. Petersburg, 199178, Russia

Abstract: Asymptotic expansions of the eigenfrequencies and eigenmodes of a thin three-dimensional elastic gasket clamped between two finite or infinite periodic rigid profiles are constructed. It is shown that the stresses are localized and concentrated near the point where the thickness of the gasket is maximal, and the character of a possible fracture is discussed. It is found that there are multiple zones of wave stopping in an elastic periodic layer and the eigenfrequencies at which elastic modes are trapped are condensed at a local perturbation of the waveguide shape.

Key words: curved elastic gasket, rigid profiles, asymptotics, eigenoscillations, concentration of stresses, periodic elastic layer, stopping zones, wave trapping.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02175


DOI: https://doi.org/10.7868/S0044466915100178

Full text: PDF file (649 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:10, 1684–1697

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 25.02.2015

Citation: S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1713–1726; Comput. Math. Math. Phys., 55:10 (2015), 1684–1697

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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