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IMA Journal of Applied Mathematics Advance Access originally published online on August 4, 2006
IMA Journal of Applied Mathematics 2006 71(5):768-782; doi:10.1093/imamat/hxl012
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© The Author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Explicit models for elastic and piezoelastic surface waves

J. Kaplunov1,**, A. Zakharov1 and D. Prikazchikov2

1 School of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK, 2 ITE Research Laboratory, Russian State Open Technical University of Railways, Chasovaya 22/2, Moscow 125993, Russia

** Email: julius.kaplunov{at}brunel.ac.uk

Explicit models for the Rayleigh and Bleustein–Gulyaev surface waves are extracted from the original 2D formulations within the general framework of linear elasticity and electroelasticity. The derivations are based on perturbing in slow time the self-similar solutions for homogeneous surface wave. Both the proposed models involve hyperbolic equations on the surface along with elliptic equations over the interior, emphasizing the dual nature of a surface wave. Comparisons with exact solutions are presented, including that for the plane Lamb problem.

Keywords: elastic; piezoelastic; surface wave; Rayleigh wave; Bleustein–Gulyaev wave.

Received on 12 July 2005. accepted on 11 January 2006.


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