On non-locally elastic Rayleigh wave

Prikazchikova; Kaplunov; Prikazchikov

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>

Citation

Kaplunov, Prikazchikov, & Prikazchikova. (2022). On non-locally elastic Rayleigh wave. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rsta.2021.0387

• 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
• Public URL: https://keele-repository.worktribe.com/output/423727
• Publisher URL: https://royalsocietypublishing.org/doi/10.1098/rsta.2021.0387