Branched flows of flexural waves in non-uniform elastic plates

Jose, Kevin, Ferguson, Neil and Bhaskar, Atul (2023) Branched flows of flexural waves in non-uniform elastic plates. PLoS ONE, 5 (1), [152]. (doi:10.1038/s42005-022-00917-z).

Record type: Article

Abstract

Flexural elastic waves and sound in solids are of great interest in wide-ranging contexts such as ultrasound in plates, geophysics, ocean engineering, aerospace and automotive structures, and musical acoustics. Despite bending waves being the most important elastic waves for such surface structures, their propagation in the presence of the inevitable non-uniformity is poorly understood. Here we show the branching and focusing behaviour of highly dispersive flexural waves travelling in elastic plates of non-uniform thickness. The thickness profile has isotropically correlated spatial randomness. The correlation length is much larger than the wavelength. The location of wave focusing shows a scaling relationship with randomness, which is consistent with those previously reported in other random media. We show this analytically and numerically. This suggests a universality in the scaling between the location of wave focusing with randomness and the correlation length, regardless of the physics of the waves in question.

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Accepted/In Press date: 16 May 2023

e-pub ahead of print date: 20 June 2023

Published date: 20 June 2023

Additional Information: Funding Information: Thanks are due to the University of Southampton for access to IRIDIS High Performance Computing; EU’s Horizon 2020 programme under Marie Skł odowska-Curie scheme (Grant Agreement No. 765636) for financial support; Dhruv Singhal for many helpful discussions; Rajiv RP Singh, Department of Physics, UC Davis for useful comments; Claus Ibsen, Vestas aircoil for providing a practical context. Funding Information: K.J. conceived the problem and performed the research. K.J. and A.B. analysed the data. K.J., N.F. and A.B. discussed the results and wrote the manuscript. A.B. and N.F. secured the funding which supported this work. Publisher Copyright: © 2022, The Author(s).