Kaplunov, J ORCID: https://orcid.org/0000-0001-7505-4546, Prikazchikov, DA ORCID: https://orcid.org/0000-0001-7682-3079 and Prikazchikova, L ORCID: https://orcid.org/0000-0001-9051-2103 (2022) On non-locally elastic Rayleigh wave. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380 (2231).

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Abstract

<jats:p>The Rayleigh-type wave solution within a widely used differential formulation in non-local elasticity is revisited. It is demonstrated that this wave solution does not satisfy the equations of motion for non-local stresses. A modified differential model taking into account a non-local boundary layer is developed. Correspondence of the latter model to the original integral theory with the kernel in the form of the zero-order modified Bessel function of the second kind is addressed. Asymptotic behaviour of the model is investigated, resulting in a leading-order non-local correction to the classical Rayleigh wave speed due to the effect of the boundary layer. The suitability of a continuous set-up for modelling boundary layers in the framework of non-local elasticity is analysed starting from a toy problem for a semi-infinite chain.</jats:p> <jats:p>This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.</jats:p>

Item Type: Article
Additional Information: The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 26 Aug 2022 15:01
Last Modified: 26 Aug 2022 15:01
URI: https://eprints.keele.ac.uk/id/eprint/11162

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