Elastic waves in fibre composite laminates

This paper considers the propagation of elastic waves in an eight-ply quasi-isotropic laminate arising from line sources of dislocation located at each of the seven interfaces in turn. The line source sets up a straight crested wave travelling along the laminate in a direction normal to the load line, and the elastodynamic equations within each layer are solved by taking the Laplace transform with respect to time and the Fourier transform with respect to the spatial coordinate in the direction of propagation. The resulting system of six first-order differential equations in each layer is 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. Examples are shown of the time history of the normal displacement of the top surface of the laminate at a distance of 20 plate thicknesses from the plane of action of the sources. The numerical inversion involves a summation over different modes of Rayleigh-Lamb waves in the laminate and contributions to the overall response from some of the individual modes are displayed.