http://dx.doi.org/10.1016/j.matpur.2015.07.004">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Nearly cloaking the elastic wave fields

Language

English

Abstract

© 2015 Elsevier Masson SAS. In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lamé system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first provide a rigorous justification of the transformation elastodynamics. Based on the blow-up-a-point construction, elastic material tensors for a perfect cloak are derived and shown to possess singularities. In order to avoid the singular structure, we propose to regularize the blow-up-a-point construction to be the blow-up-a-small-region construction. However, it is shown that without incorporating a suitable lossy layer, the regularized construction would fail due to resonant inclusions. In order to defeat the failure of the lossless construction, a properly designed lossy layer is introduced into the regularized cloaking construction. We derive sharp asymptotic estimates in assessing the cloaking performance. The proposed cloaking scheme is capable of nearly cloaking an arbitrary content with a high accuracy.

Keywords

Asymptotic estimates, Elastic cloaking, Lamé system, Regularization, Transformation elastodynamics

Publication Date

2015

Source Publication Title

Journal de Mathématiques Pures et Appliquées

Publisher

Elsevier

ISSN (print)

00217824

ISSN (electronic)

17763371

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