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.

Application of the Value Optimization Model of Key Factors Based on DSEM

“…If the wave amplitude attenuation at the interface is known, the constraint function of the size of bounded medium is transformed from function (15). Consider…”

“…In its practical application, the DSEM was applied to analyze the soil-structure interaction with fractional order [10], the nonlinear overload of the unbounded medium-arch dam [11], the impact of pile driving vibration on seawall [12], and fluid-structure dynamic interaction [13]. In the evaluation of key factors, the causes of the error of the DSEM had been analyzed and described in detail in [14][15][16]. Simultaneously, the key factors estimated in [17][18][19] have a great influence on the accuracy of the soilstructure interaction.…”