On Rayleigh-type surface waves in an initially stressed

incompressible elastic solid

M. ShamsCentre for Advanced Mathematics

National University of Sciences and Technology, Sector H12, Islamabad, Pakistan

R. W. OgdenSchool of Engineering, University of Aberdeen

King’s College, Aberdeen AB24 3UE, United Kingdom

and

School of Mathematics and Statistics, University of Glasgow

Glasgow G12 8QW, United Kingdom

Abstract

In this paper, we apply the theory of the superposition of infinitesimal defor-mations on finite deformations in an initially stressed hyperelastic material to thestudy of the propagation of surface waves in an initially stressed incompressiblehalf-space subjected to a pure homogeneous deformation. This is based on a the-ory of initial stress in elastic solids due to Shams et al. (2011). The initial stressis not itself associated with a finite elastic deformation and this contrasts with thesituation in which the initial stress is a pre-stress that is accompanied by a finitedeformation. A general formulation of the equations governing incremental motionsis provided, and then specialized to two-dimensional motions in a principal planeof the underlying (homogeneous) deformation with a uniform initial stress that iscoaxial with the finite deformation. With this specialization, the combined effectof initial stress and finite deformation on the speed of Rayleigh waves is discussedand illustrated graphically with the main emphasis on the effect of initial stress.

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