Non-linear propagation of waves induced by general vibrations of plates

Abstract

First-order uniform expansions for the non-linear propagation of waves induced by general motions of plates are obtained. The method of renormalization is used to determine the non-linear propagation of two waves and 2 N waves in a lossless medium. The strained co-ordinates contain terms that account for the effects of self-interaction and mutual interaction of the waves. The mutual interaction terms are negligible if the induced waves are pulses or periodic functions. The method of multiple scales is used to determine the propagation of two waves in a thermoviscous medium. The result consists of two uncoupled equations that can be reduced to Burgers' equations. They account for the effects of dissipation and self-interaction of the waves but not the effects of mutual interaction. A combination of the methods of renormalization and multiple scales can be used to account for dissipation and all interactions.