Transient response of quasi-isotropic fiber composite laminates to internal line sources

Abstract

This article 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 laminate is composed of identical layers of a fiber composite material which is modeled as a homogeneous transversely isotropic elastic continuum with the axis of transverse isotropy along the fiber direction. The line source sets up a straight crested wave traveling along the laminate in the 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. The graphs presented show the time history of the normal displacement of the top surface of the laminate at distances of 1 and 20 plate thicknesses from the plane of action of the sources. These graphs are for four different orientations of the line of action of the sources, namely, at angles 0, 30, 60, and 90 degrees to the fiber direction in the surface layer. The numerical inversion involves a summation over different modes of Rayleigh-Lamb waves in the laminate and results are also presented showing the contributions to the overall response from some of the individual modes.