Influence of the Ground Acceleration Variation Mode on the Linear Elastic Response Spectrum

Abstract

This work focuses on comparing the seismic response spectrum of El Centro obtained under two different assumptions about the nature (linear variation and constant mean) of the ground acceleration over a time increment. This research proposes a quasi-analytical approach to solving the differential equation of motion of a simple oscillator forced by an earthquake, combining trigonometric relationships and integration by parts theories. The generated differential equation is solved using the Duhamel integral, making two assumptions about the ground acceleration. An iterative calculation allows us to obtain the different points of the time displacement and then construct the oscillation curves (displacements) as a function of time. The response spectrum is constructed using the maxima of the oscillation curves and their corresponding periods for the same damping ratio. The other spectral curves are obtained by repeating the same scenario as many times as there are damping ratios, and for each assumption. Comparison of the results shows that the maxima of the oscillator responses correspond to the same periods, and that apart from the difference between the responses of the spectral curves at zero damping ratio, the other spectral responses are similar for non-zero damping ratios. Furthermore, the difference between the spectral responses is so small for the first curves and so negligible for the others that both approaches lead to similar results.