Singular perturbations and cloaking illusions for elastic waves in membranes and Kirchhoff plates

TL;DR

This paper investigates how boundary conditions affect cloaking effectiveness for elastic waves in membranes and Kirchhoff plates, revealing limitations of cloaking due to boundary constraints.

Contribution

It provides an analytical study of boundary condition effects on elastic wave cloaking in membranes and plates, highlighting conditions that hinder cloaking performance.

Findings

Dirichlet boundary condition reduces cloaking in membranes

Cloaking becomes impossible for Kirchhoff plates under certain conditions

Explicit solutions illustrate boundary effects on wave propagation

Abstract

A perturbation approach is used for analysis of a near-cloak in shielding a finite scatterer from an incident flexural wave. The effect of the boundary conditions on the interior surface of the cloaking layer is analysed in detail, based on the explicit analytical solutions of a wave propagation problem for a membrane as well as a Kirchhoff flexural plate. It is shown that the Dirichlet boundary condition on the interior contour of the cloak significantly reduces the cloaking action in the membrane case, and it also makes cloaking impossible for flexural waves in a Kirchhoff plate.