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Higher-order WKB analysis of reflection from tapered elastic wedges

Higher-order WKB analysis of reflection from tapered elastic wedges
Higher-order WKB analysis of reflection from tapered elastic wedges
The reflection coefficient for a one-dimensional elastic wedge driven from an adjacent uniform plate is analysed using higher-order WKB-method matrix analysis and the results are compared with numerical simulations using Finite Elements. The numerical results are correctly predicted by the WKB analysis above a certain frequency. In general, this frequency is shown to fall as the order of the WKB analysis approximation is increased, but at least a second-order WKB approximation is required in the working
frequency range. The total reflection coefficient depends not only on the practical truncation of the wedge but also on the discontinuity between the wedge and the plate to which it is attached. Interference between these two sources of reflection causes ripples in the total reflection coefficient. Apart from the usual power-law profile, alternative thickness variations are also considered. Limitations on the applicability of the analytical method are illustrated through a wedge whose thickness varies predominantly away from the junction between the wedge and the uniform plate.
Non-uniform plate, WKB, Wedge, Reflection, Higher-order approximation, Acoustic black hole
0022-460X
368-388
Karlos, Angelis
ed53f118-9719-4f58-a1eb-bd4d67df3a27
Elliott, Stephen J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Cheer, Jordan
8e452f50-4c7d-4d4e-913a-34015e99b9dc
Karlos, Angelis
ed53f118-9719-4f58-a1eb-bd4d67df3a27
Elliott, Stephen J.
721dc55c-8c3e-4895-b9c4-82f62abd3567
Cheer, Jordan
8e452f50-4c7d-4d4e-913a-34015e99b9dc

Karlos, Angelis, Elliott, Stephen J. and Cheer, Jordan (2019) Higher-order WKB analysis of reflection from tapered elastic wedges. Journal of Sound and Vibration, 449, 368-388. (doi:10.1016/j.jsv.2019.02.041).

Record type: Article

Abstract

The reflection coefficient for a one-dimensional elastic wedge driven from an adjacent uniform plate is analysed using higher-order WKB-method matrix analysis and the results are compared with numerical simulations using Finite Elements. The numerical results are correctly predicted by the WKB analysis above a certain frequency. In general, this frequency is shown to fall as the order of the WKB analysis approximation is increased, but at least a second-order WKB approximation is required in the working
frequency range. The total reflection coefficient depends not only on the practical truncation of the wedge but also on the discontinuity between the wedge and the plate to which it is attached. Interference between these two sources of reflection causes ripples in the total reflection coefficient. Apart from the usual power-law profile, alternative thickness variations are also considered. Limitations on the applicability of the analytical method are illustrated through a wedge whose thickness varies predominantly away from the junction between the wedge and the uniform plate.

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Accepted/In Press date: 26 February 2019
e-pub ahead of print date: 4 March 2019
Published date: 9 June 2019
Keywords: Non-uniform plate, WKB, Wedge, Reflection, Higher-order approximation, Acoustic black hole

Identifiers

Local EPrints ID: 429086
URI: https://eprints.soton.ac.uk/id/eprint/429086
ISSN: 0022-460X
PURE UUID: da426d87-2857-45dd-a559-7e5ba1a31a63
ORCID for Jordan Cheer: ORCID iD orcid.org/0000-0002-0552-5506

Catalogue record

Date deposited: 20 Mar 2019 17:30
Last modified: 21 Mar 2019 01:31

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