Abstract

Nonlinear Interaction of Two Codirectional Surface SH Waves on a Layered Elastic Half Space

M.Teymur (Department of Mathematics, Istanbul Technical University, Istanbul, Turkey)

e-mail: teymur@itu.edu.tr

In this work the effect of nonlinearity on the interaction of two codirectional quasiharmonic surface SH (Shear Horizontal) waves propagating on a layered half space is examined. In the analysis it is assumed that the half space is covered by a different nonlinear elastic layer of uniform and finite thickness, the free surface of the layered half space is free of traction and displacements and stresses are continuous at the interface between the layer and the half space. Then, the propagation of two codirectional nonlinear quasiharmonic waves centered around two different wave numbers is considered. The problem is examined by employing the method of multiple scales. It is found that the first order slowly varying amplitudes of the interacting waves are governed by two coupled NLS (Nonlinear Schrodinger) equations. From these general interaction equations, the coupled equations which govern the nonlinear interaction of two codirectional waves having equal group velocities and the coupled equations describing the fifth or higher order harmonic resonances are also obtained. Then the instabilities and the existence of multiphase solitary envelope solutions are discussed .

Section : 1