Surface shear horizontal waves in a double-layered nonlinear elastic half space

Abstract

The method of multiple scales is used to examine the slow modulation of a harmonic surface shear horizontal wave over the surface of a non-linear elastic half space covered with two different non-linear elastic layers of uniform thickness. The appropriate non-linear Schrodinger (NLS) equation is derived with coefficients that depend, in a complicated way, on linear and non-linear material parameters of the double-layered half space, the thicknesses of the layers and also the wave number of the waves. This equation reduces to the NLS equation obtained for the case of a single-layered half space when the thickness of one of the layers goes to zero. Finally, the effect of the non-linear properties of the intermediate layer on the existence of solitary waves has been investigated numerically and the results are presented graphically. Also, to reveal the effect of the second layer, the coefficients of the NLS equations obtained for a double-layered half space and for a single-layered half space are compared. It has been observed that the propagation is affected considerably by the existence of a second layer.