FORMULATION OF THE TIME-VARYING FUNCTION OF MOMENTARY ENERGY INPUT TO A SINGLE-DEGREE-OF-FREEDOM SYSTEM USING FOURIER SERIES

Abstract

This article derives a time-varying function of the momentary energy input to a linear elastic single-degree-of-freedom system with viscous and complex damping. The problem is formulated in the form of a Fourier series using the Fourier amplitude and the difference of Fourier phase angles. The numerical analysis results show that (1) the time-varying function formulated using the Fourier series corresponds to the envelope of ground acceleration, and (2) the maximum momentary input energy evaluated using the formulation in this paper agrees well with that obtained from time-history analysis.