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Computational Mathematics and Mathematical Physics

, Volume 55, Issue 10, pp 1684–1697 | Cite as

Eigenmodes of a thin elastic layer between periodic rigid profiles

  • S. A. NazarovEmail author
Article
  • 33 Downloads

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.

Keywords

curved elastic gasket rigid profiles asymptotics eigenoscillations concentration of stresses periodic elastic layer stopping zones wave trapping 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.St. Petersburg State UniversityPeterhof, St. PetersburgRussia
  2. 2.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

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