Branched flows of flexural elastic waves in non-uniform cylindrical shells
Branched flows of flexural elastic waves in non-uniform cylindrical shells
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance, and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour-consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for waves in other physical contexts, as well as dispersive flexural waves in elastic plates.
Jose, Kevin
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Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
26 May 2023
Jose, Kevin
f4b1bda1-3c49-4c48-82cc-f7456e65ee22
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Jose, Kevin, Ferguson, Neil and Bhaskar, Atul
(2023)
Branched flows of flexural elastic waves in non-uniform cylindrical shells.
PLoS ONE, 18 (5), [e0286420].
(doi:10.1371/journal.pone.0286420).
Abstract
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance, and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour-consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for waves in other physical contexts, as well as dispersive flexural waves in elastic plates.
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journal.pone.0286420
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Accepted/In Press date: 16 May 2023
Published date: 26 May 2023
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Local EPrints ID: 501265
URI: http://eprints.soton.ac.uk/id/eprint/501265
ISSN: 1932-6203
PURE UUID: d5e5d9eb-0cce-45fb-b7b8-c8f05e0601b4
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Date deposited: 28 May 2025 16:35
Last modified: 22 Aug 2025 01:33
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Kevin Jose
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