A computational method for wave propagation from a point load in an anisotropic material

One approach which is employed to solve dynamic point load problems in plat es and laminates is to take integral transforms to reduce the governing equ ations to a system of ordinary differential equations with respect to the d epth variable. The solution of this system leads to expressions for the tra nsforms of the displacement and stress components at any level in the plate and the transient response at any location may then be recovered by invers ion of the multiple transforms. The formal transform inversion involves a d ouble infinite integral but by making a change of variable this may be repl aced by an infinite integral associated with a line source and a finite int egral with respect to the orientation of the line. A first attempt at apply ing this approach to obtain the point load response of quasi-isotropic fibr e composite laminate led to a non-causal predicted signal. This paper deals with an investigation of this proposed method applied to the simpler model problem of wave propagation in a two-dimensional anisotropic medium. Resul ts are obtained for two different time histories of point loads, namely: a delta function; and a single period of a sine function. In the case of the delta function source a comparison is made with the analytic solution and t he errors arising from the numerical approach are discussed. Graphs are als o presented showing the non-causal contributions to the overall response wh ich arise at individual angles of orientation of the line source. (C) 2000 Elsevier Science B.V. All rights reserved.