Two-dimensional wave packets in an elastic solid with couple stresses

Babaoglu C., Erbay S.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.39, no.6, pp.941-949, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 6
  • Publication Date: 2004
  • Doi Number: 10.1016/s0020-7462(03)00076-3
  • Page Numbers: pp.941-949


The problem of (2+1) (two spatial and one temporal) dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses is considered. The aim is to derive (2+1) non-linear model equations for the description of elastic waves in the far field. Using a multi-scale expansion of quasi-monochromatic wave solutions, it is shown that the modulation of waves is governed by a system of three non-linear evolution equations. These equations involve amplitudes of a short transverse wave, a long transverse wave and a long longitudinal wave, and will be called the "generalized Davey Stewartson equations". Under some restrictions on parameter values, the generalized Davey-Stewartson equations reduce to the Davey-Stewartson and to the non-linear Schrodinger equations. Finally, some special solutions involving sech-tanh-tanh and tanh-tanh-tanh type solitary wave solutions are presented. (C) 2003 Elsevier Ltd. All rights reserved.