Trapped modes in an elastic plate with a hole

Förster, C.; Weidl, T.

doi:10.1090/S1061-0022-2011-01192-6

Trapped modes in an elastic plate with a hole
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by C. Förster and T. Weidl
Translated by: V. Sloushch

St. Petersburg Math. J. 23 (2012), 179-202

DOI: https://doi.org/10.1090/S1061-0022-2011-01192-6

Published electronically: November 10, 2011

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Abstract:

For an infinite linear elastic plate with stress-free boundary, the trapped modes arising around holes in the plate are investigated. These are $L^2$-eigenvalues of the elastostatic operator in the punched plate subject to Neumann type stress-free boundary conditions at the surface of the hole. It is proved that the perturbation gives rise to infinitely many eigenvalues embedded into the essential spectrum. The eigenvalues accumulate to a positive threshold. An estimate of the accumulation rate is given.

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