Colquitt, DJ and Brun, M and Gei, M and Movchan, AB and Movchan, NV and Jones, IS (2014) Transformation elastodynamics and cloaking for flexural waves. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 72. pp. 131-143. ISSN 0022-5096
1401.7579v1.pdf - Accepted Version
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The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing exural 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 square cloak for exural 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.
Keywords: cloaking, transformation elastodynamics, plates, invisibility
|Uncontrolled Keywords:||01 Mathematical Sciences, 02 Physical Sciences, 09 Engineering|
|Subjects:||Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
|Divisions:||Maritime and Mechanical Engineering|
|Date Deposited:||03 Jun 2015 10:22|
|Last Modified:||15 Nov 2016 11:46|
|DOI or Identification number:||10.1016/j.jmps.2014.07.014|
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