Two-dimensional wave packets in an elastic solid with couple stresses
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CitationBabaoğlu, C. & Erbay, S. (2004). Two-dimensional wave packets in an elastic solid with couple stresses. International Journal of Non-Linear Mechanics, 39(6), 941-949. doi:10.1016/S0020-7462(03)00076-3
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.
SourceInternational Journal of Non-Linear Mechanics
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