Eigenmodes of a thin elastic layer between periodic rigid profiles

S. A. Nazarov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1713-1726

Résumé

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.

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