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IMA Journal of Applied Mathematics Advance Access originally published online on August 16, 2007
IMA Journal of Applied Mathematics 2007 72(6):730-747; doi:10.1093/imamat/hxm018
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Surface waves supported by thin-film/substrate interactions

D. J. Steigmann

Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA

R. W. Ogden{dagger}

Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK

{dagger} Email: rwo{at}maths.gla.ac.uk

Received on January 23, 2007; Accepted on April 20, 2007

A systematic approximation to the linear equations for small-amplitude surface waves in an elastic half space, interacting with a residually stressed thin film of different material bonded to its plane boundary, is developed in powers of the film thickness, assuming the latter to be small compared to the wavelength of the disturbance. The theory is illustrated by calculating asymptotic expansions of the wave speeds for Love and Rayleigh waves valid to second order in the dimensionless film thickness for a transversely isotropic film bonded to an isotropic substrate.

Keywords: Surface waves; thin films; film/substrate interactions.


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