Transformation elastodynamics and cloaking for flexural waves

Colquitt, D. J., Brun, M., Gei, M. ORCID: https://orcid.org/0000-0003-3869-7504, Movchan, A. B., Movchan, N. V. and Jones, I. S. 2014. Transformation elastodynamics and cloaking for flexural waves. Journal of the Mechanics and Physics of Solids 72 , pp. 131-143. 10.1016/j.jmps.2014.07.014

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Abstract

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
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Additional Information:	Available online 14 August 2014
Publisher:	Elsevier
ISSN:	0022-5096
Date of Acceptance:	28 July 2014
Last Modified:	28 Oct 2022 09:17
URI:	https://orca.cardiff.ac.uk/id/eprint/74029

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