Channelling of elastic waves in an eight-ply fiber composite plate

Abstract

The paper is concerned with the channeling of elastic waves propagating in an eight-ply quasi-isotropic laminate arising from impulsive line sources of dislocation located at each of the seven interfaces in turn. The laminate is composed of identical layers of fiber composite material which is modeled as a transversely isotropic continuum with the axis of transverse isotropy along the fiber direction. The line sources set up a straight crested wave travelling along the laminate in the direction normal to the load line and the elastodynamic equations within each layer are solved by taking Laplace transforms with respect to time and Fourier transforms with response to the co-ordinate in the propagation direction. The resulting system of six first order differential equations in each layer are solved to obtain the transforms of the displacement and stress components throughout the laminate. The time history of any displacement or stress component at any location may then be recovered by numerical inversion of the double transform. This numerical inversion involves a summation over the normal modes of Rayleigh-Lamb waves and in an earlier paper, it has been shown that for some locations of the line source, the contribution to the upper surface normal displacement from the fundamental mode is swamped by contributions from some of the higher modes. Here, details are presented of the displacement variation through the laminate associated with the different Rayleigh-Lamb modes showing how the disturbance is channelled in some layers for specific locations of the source line.