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DC Field | Value | Language |
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dc.contributor.author | Lawrie, JB | - |
dc.date.accessioned | 2023-08-09T13:35:29Z | - |
dc.date.available | 2023-08-09T13:35:29Z | - |
dc.date.issued | 2023-09-13 | - |
dc.identifier | ORCID iD: Jane B Lawrie https://orcid.org/0000-0003-3674-5605 | - |
dc.identifier.citation | Lawrie, J.B. (2023) 'Edge Resonance: Exact Results and Fresh Insights', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 0 (accepted, in press), pp. 1 - 23. doi: 10.1098/rspa.2023.0256 (pending) | en_US |
dc.identifier.issn | 1364-5021 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/26929 | - |
dc.description | Data Accessibility: This article has no additional data. | en_US |
dc.description | Declaration of AI use: I have not used AI-assisted technologies in creating this article. | - |
dc.description.abstract | Copyright © 2023 The Author. The eigensystem underpinning the classical edge resonance phenomenon in linear elasticity is studied. Several exact results are presented, the most significant being an identically zero sum demonstrating the linear dependence of the stresses. An exact condition for edge resonance is derived. This is cast into a form that is independent of the Lamb modes, robust and highly convergent, enabling the system to be explored by varying Poisson’s ratio (PR) or frequency. An improved estimate of the value of PR for real resonance is determined, as is the non-Lamé frequency corresponding to resonance when PR is zero. Quasi-resonances are explored. It is demonstrated that, for fixed PR, these occur at more than one frequency, and that they occur for negative PR. It is shown that quasi-resonances are associated with one of two distinct families of complex resonances: real PR and complex frequency or real frequency and complex PR. Higher Lamé frequencies are considered. It is demonstrated that a real pure shear resonance exists at the second Lamé frequency when PR is zero. The corresponding edge displacement is simple in form, and it is anticipated that such resonances exist at every Lamé frequency. Finally, point-wise convergence for Lamb-mode eigenfunction expansions is established. | en_US |
dc.description.sponsorship | No funding for this study. | en_US |
dc.format.medium | Print-Electronic | - |
dc.language.iso | en | en_US |
dc.publisher | Royal Society Publishing | en_US |
dc.rights | Copyright © The Author 2023. Published by the Royal Society under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. | - |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | - |
dc.subject | edge resonance | en_US |
dc.subject | Lamb modes | en_US |
dc.subject | quasi-resonance | en_US |
dc.subject | complex resonance | en_US |
dc.subject | point-wise convergence | en_US |
dc.title | Edge Resonance: Exact Results and Fresh Insights | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.1098/rspa.2023.0256 | - |
dc.relation.isPartOf | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | - |
pubs.issue | 2277 | - |
pubs.publication-status | Published | - |
pubs.volume | 479 | - |
dc.identifier.eissn | 1471-2946 | - |
dc.rights.holder | The Author | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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File | Description | Size | Format | |
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FullText.pdf | Copyright © The Author 2023. Published by the Royal Society under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. | 1.59 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License