Nonlinear modulation of surface sh waves in a double layered elastic half space

Abstract

The nonlinear shear horizontal (SH) surface waves in an elastic half space coated with two different layers of uniform thickness are examined. The half space and both layers are assumed to be homogeneous, isotropic, incompressible, elastic and having different mechanical properties. In the analysis it is assumed that linear shear velocity of the top layer is slower than velocities of the internal layer and the half space. By employing the method of multiple scales, it is shown that nonlinear modulation of SH waves is governed asymptotically by a nonlinear Schrödinger (NLS) equation. The coefficients of this equation depend on, in a complicated way, on linear and nonlinear material parameters of the layered half space, the thicknesses of the layers and also the wave number of the waves. The effect of the existence of a second layer on the existence of solitary waves has been investigated numerically. Also a comparison between the coefficients of the NLS equation for the double layered half space and that of a single layered half space has been made. It is remarked that the existence of the envelope and dark solitons is affected strongly by the nonlinear material parameter of the top layer.