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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on June 3, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2008 61(3):353-371; doi:10.1093/qjmam/hbn013
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Q. Jl Mech. Appl. Math, Vol. 61. No. 3 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Large-amplitude love waves

E. Rodrigues Ferreira and Ph. Boulanger{dagger}

( Département de Mathématique, Université Libre de Bruxelles, Campus Plaine CP218/1, 1050 Bruxelles, Belgium )

M. Destrade

( Institut Jean Le Rond d'Alembert, CNRS (UMR7190), Université Pierre et Marie Curie, Case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France )

{dagger} <phboul{at}ulb.ac.be>

Received 22 October 2007. Revise 22 April 2008.
  Abstract

In the context of the finite elasticity theory, we consider a model for compressible solids called ‘compressible neo-Hookean material’. We show how finite-amplitude inhomogeneous plane wave solutions and finite-amplitude unattenuated solutions can combine to form a finite-amplitude Love wave. We take a layer of finite thickness overlying a solid half-space, both made of different prestressed compressible neo-Hookean materials. We derive an exact solution of the equations of motion and boundary conditions and also obtain results for the energy density and the energy flux of the waves. Finally, we investigate the special case when the interface between the layer and the substrate is in a principal plane of the prestrain. A numerical example is given.


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