Kaplunov J, Prikazchikov D A, Prikazchikova L
School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UK.
Philos Trans A Math Phys Eng Sci. 2022 Sep 5;380(2231):20210387. doi: 10.1098/rsta.2021.0387. Epub 2022 Jul 18.
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. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
