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

TL;DR

This paper investigates how local modifications to Young's modulus in an elastic plate cause the emergence and accumulation of infinitely many eigenvalues within the essential spectrum, providing estimates on their distribution.

Contribution

It demonstrates the existence of infinitely many eigenvalues due to local perturbations of Young's modulus and analyzes their asymptotic behavior and accumulation rate.

Findings

Infinitely many eigenvalues arise from local Young's modulus changes

Eigenvalues accumulate at a positive threshold

Provides estimates on eigenvalue distribution and asymptotics

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.