NONLINEAR MODULATION OF A WAVE TRAIN IN A N ELASTIC STRUCTURE

Composite structures formed by an infinite elastic thin plate placed o n elastic foundation are uniform waveguides enables to focus a high en ergy density in order that nonlinearities can be excited. This class o f elastic structures is an interesting candidate for the real observat ion of two-dimensional wave trains or packets with a soliton-shape env elope in elastic solids. The purpose of this contribution is to study the influences of the geometric dispersion and material nonlinearities of the elastic substrat on the modulation of flexural waves in this s imple test structure. The analysis is restricted to excitations which consist of slowly varying envelope in space and time modulating a harm onic carrier wave. In the case of small perturbations the problem thus posed is solved by using the technique of multiple scales. It is show n at the lowest of the secularity conditions, the complex amplitude of the envelope satisfies a 2-D nonlinear Schrodinger equation with the nonlinear coefficient as a function of the wave number and the sign of the nonlinearity. Particular solutions of this equation namely gray o r dark solitons are given and illustrated for a circurlar frequency of the carrier wave close of the linear spectrum gap.