Propagation of steady nonlinear waves in a coated elastic half-space

We consider propagation of nonlinear travelling waves in a coated elastic h alf-space. Both the coating and half-space are composed of neo-Hookean mate rials which have the same density but different shear moduli <(<mu>)over ca p> and mu, respectively. We use r = <(<mu>)over cap>/mu as a tuning paramet er with the limit r --> 1 corresponding to a single half-space. When r - 1 = O(1) the bonded structure is strongly dispersive and it is well known tha t any strongly dispersive medium can mathematically support a nonlinear sin usoidal wave (i.e. a Stokes wave) although such a wave may not be stable. W e focus our attention on the case when r - 1 is small (so that the coated h alf-space is weakly dispersive). In this case single mode waves are not pos sible and we look for multiple-mode travelling wave solutions in which the surface elevation takes the form of a Fourier expansion. We find that a fam ily of such multiple-mode nonlinear waves can indeed exist. Their propertie s and the effects of a uni-axial compression are investigated. (C) 2001 Els evier Science B.V. All rights reserved.