Chebakov, R, Kaplunov, J and Rogerson, GA ORCID: https://orcid.org/0000-0003-0264-2931 (2016) Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects. Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, 472 (2186).

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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.

Item Type: Article
Additional Information: Published as; Chebakov, R., Kaplunov, J. & Rogerson, G.A., 2016. Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 472(2186), p.20150800. Available at: http://dx.doi.org/10.1098/rspa.2015.0800.
Uncontrolled Keywords: non-local, elasticity, asymptotic, boundary conditions, Rayleigh wave, inhomogeneous
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 02 Mar 2016 11:47
Last Modified: 15 Apr 2019 11:26
URI: http://eprints.keele.ac.uk/id/eprint/1516

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