Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Kaplunov

doi:10.1098/rspa.2015.0800

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

Kaplunov

Authors

Julius Kaplunov j.kaplunov@keele.ac.uk

Abstract

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the ‘local’ problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Acceptance Date	Jan 11, 2016
Publication Date	Feb 10, 2016
Journal	Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences
Print ISSN	1364-5021
Publisher	The Royal Society
DOI	https://doi.org/10.1098/rspa.2015.0800
Keywords	non-local, elasticity, asymptotic, boundary conditions, Rayleigh wave, inhomogeneous
Publisher URL	http://dx.doi.org/10.1098/rspa.2015.0800