Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates



Misseroni, D, Movchan, AB and Bigoni, D
(2019) Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 475 (2229). 20190283-.

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Abstract

In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analysed, but still unchallenged, mechanical problem. The 'cloaking transformation' concept, originally developed in electromagnetism and optics, is not directly applicable to elastic waves, displaying a complex vectorial nature. Consequently, all examples of elastic cloaking presented so far involve complex design and thick coating skins. These cloakings often work only for problems of unidirectional propagation, within narrow ranges of frequency, and considering only one cloaked object. Here, a new method based on the concept of reinforcement, achieved via elastic stiffening and mass redistribution, is introduced to cloak multiple voids in an elastic plate. This simple technique produces invisibility of the voids to flexural waves within an extremely broad range of frequencies and thus surpassing in many aspects all existing cloaking techniques. The proposed design principle is applicable in mechanical problems ranging from the micro-scale to the scale of civil engineering. For instance, our results show how to design a perforated load-bearing building wall, vibrating during an earthquake exactly as the same wall, but unperforated, a new finding for seismic protection.

Item Type: Article
Additional Information: 16 pages, 5 figures
Uncontrolled Keywords: cloaking, structured plates, waves, scattering reduction
Depositing User: Symplectic Admin
Date Deposited: 10 Mar 2020 14:39
Last Modified: 18 Jan 2023 23:58
DOI: 10.1098/rspa.2019.0283
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3078319