Trapped modes for the elastic plate with a perturbation of Young's modulus

Abstract

We consider a linear elastic plate with stress-free boundary conditions in the limit of vanishing Poisson coefficient. We prove that under a local change of Young's modulus infinitely many eigenvalues arise in the essential spectrum which accumulate at a positive threshold. We give estimates on the accumulation rate and on the asymptotical behaviour of the eigenvalues.

24 pages

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