Wave Motion 36 (2002) 1–21 An expansion method for non-linear Rayleigh waves

We use ideas from analytic bifurcation theory to develop expansions for periodic small amplitude traveling surface elastic waves of permanent form in the half-plane (Rayleigh waves). We focus on the case of hyperelastic materials where the traveling wave problem has a variational structure, and solve numerically the equations describing the lowest order approximation to the traveling wave solutions. For the materials considered, there is evidence for solutions describing elastic displacements that have discontinuous derivative at the boundary of the domain. © 2002 Published by Elsevier Science B.V. 1