AN IMPROVEMENT TO THE FOURIER SERIES METHOD FOR INVERSION OF LAPLACE TRANSFORMS APPLIED TO ELASTIC AND VISCOELASTIC WAVES

Abstract

A parametric study of composite strips leads to systems of partial differential equations, coupled through interface conditions, that are naturally solved in Laplace transform space. Because of the complexity of the solutions in transform space and the potential variations due to geometry and materials, a systematic approach to inversion is necessarily numerical. The Dubner-Abate-Crump (DAC) algorithm is the standard in such problems and is implemented. The presence of discontinuous wavefronts in the problems considered leads to Gibbs phenomenon; which, in turn, overestimates the values of maximum stress. These errors are mitigated by use of Lanczos' σ-factors, which combine naturally with the DAC algorithm.