Complex frequencies in elastodynamics, with application to the Damping-Solvent Extraction method

Abstract

This paper addresses the use of complex frequencies in problems of wave propagation and structural vibrations. The most common form of application is as artificial damping that is extracted after the response in the time domain has been obtained. Then again a rather unorthodox application is in the simulation of systems of infinite spatial extent by means of finite systems modeled with discrete methods such as finite elements, a task that can be accomplished even when no transmitting or absorbing boundaries are used. This latter application of complex frequencies, which goes by the name damping-solvent extraction method or its acronym DSE, is assessed herein by means of exact solutions to canonical problems that are used to establish the conditions that must be met by the finite models to work as intended, especially the size of the models, the magnitude of the imaginary component of frequency, and the limitations of the method.