Transformation elastodynamics and cloaking for flexural waves

Colquitt, DJ ORCID: 0000-0001-5637-1626, Brun, M, Gei, M, Movchan, AB, Movchan, NV and Jones, IS ORCID: 0000-0002-5226-0053
(2014) Transformation elastodynamics and cloaking for flexural waves. Journal of the Mechanics and Physics of Solids, 72. pp. 131-143.

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The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.

Item Type: Article
Additional Information: archiveprefix: arXiv arxivid: 1401.7579 keywords: Cloaking,Invisibility,Metamaterials Waves,Plates,Transformation elastodynamics bdsk-url-1:
Uncontrolled Keywords: cloaking, transformation elastodynamics, plates, invisibility, metamaterials, waves
Subjects: ?? QA ??
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Depositing User: Symplectic Admin
Date Deposited: 22 Dec 2015 15:31
Last Modified: 16 Dec 2022 04:43
DOI: 10.1016/j.jmps.2014.07.014
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