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On non-locally elastic Rayleigh wave

Prikazchikova; Kaplunov; Prikazchikov

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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>

Acceptance Date Mar 16, 2022
Publication Date Sep 5, 2022
Journal Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-503X
Publisher The Royal Society
DOI https://doi.org/10.1098/rsta.2021.0387
Publisher URL https://royalsocietypublishing.org/doi/10.1098/rsta.2021.0387

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