An Approximate Procedure for the Solution of a Class of Transient-Wave Diffraction Problems

Abstract

The description of even the gross features of the response to an incident stress pulse of an infinite elastic solid with a hole or obstruction requires very extensive calculations [1]. On the other hand, the response of such elastic systems to a harmonic incident wave is much less intricate. It is well known that the response to any given incident pulse can be constructed from the solution of the harmonic wave problem. Furthermore, it is clear that the computational difficulty associated with this synthesis can be reduced enormously when a suitable, algebraically simple approximation to the harmonic response can be found. In this paper, a useful rule for choosing the appropriate approximation to the harmonic wave response is presented. This method is shown to give results in agreement with known solutions. The procedure is also applied to problems where only solutions to the harmonic wave case are available. The most important potential use of the technique lies in the possibility that, for some classes of structures, one may be able to identify the parameters of the approximate harmonic response with simple macroscopic properties of the system. Such an identification would not only save much labor but would also identify design criteria for the optimization of the system.