Abstract

Nonlinear Modulation of Rayleigh Waves in a Layered Elastic Half Space

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

e-mail: ahmetola@itu.edu.tr

In this work the propagation of small but finite amplitude Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. It is assumed that the constituent materials are compressible, the free boundary of the layered half-space is free of tractions and stresses and displacements are continuous at the interface between the layer and the half-space. Then the nonlinear self modulation of a group of Rayleigh waves centered around a wave number and a frequency is considered. The amplitude of the waves are assumed to be small but finite and the problem is investigated by employing a perturbation method, namely, the method of multiple scales. It is then shown that the first order slowly varying amplitude of the wave modulation is governed by a standart NLS ( Nonlinear Schrodinger ) equation. Since the solutions of the NLS equation strongly depend on the sign of the product of its coefficients, the numerical evaluation of the variation of this quantity with the wave number is performed by giving appropriate values to the material constants. Then the stability condition is discussed and the existence of bright (envelope) and dark solitons is manifested.

Section : 1