Formulation of the Time-Varying Function of Momentary Energy Input to a SDOF System by Fourier Series

Abstract

In this article, the time-varying function of ground acceleration is formulated by using Fourier amplitude and the difference of Fourier phase angle. Then the time-varying function of the momentary energy input, proposed by Inoue and his co-authors, to a linear elastic SDOF system with viscos and complex damping is formulated in the form of Fourier series. The numerical analysis results show that (1) the time-varying function formulated using Fourier series corresponds to the envelope of ground acceleration, and (2) the maximum momentary input energy evaluated from formulation in this paper agrees well to that obtained from time-history analysis results.