Abstract

Abstract

As it is widely known nonlinear dynamic analyses are mostly carried out in the time domain. In this paper an alternate procedure to carry out nonlinear computations in the frequency domain is proposed. This method is a powerful extension of the widely known equivalent nonlinear method that takes into account approximately the dynamic nonlinearities of the soil behavior using the complex response approach. There is no doubt that true nonlinear dynamic analyses can only be carried out in the time domain, where the dynamic material properties (mainly the dynamic material stiffness) are modified every time step. Accordingly, the stiffness matrix must be modified and hence the dynamic equation’s system has to be solved again for each new time step. Obviously, nonlinear analysis of large structures subject to strong seismic events will require great amounts of computer time, which hinder detailed studies to pinpoint the variables that control the behavior of complex structural problems. Accordingly, a new simple yet accurate procedure to perform nonlinear and linear structural analyses was developed and is presented in this paper. It consists in dividing the excitation time history in a specific number of stretches (windows in the time domain) and applying the Short-Time Fourier Transform to each window to map them into the frequency domain. The analysis is performed marching forward along the resulting frequency stretches, considering that the excitation is integrated by the power spectral density of the signal-stretch we are positioned in the frequency domain and the corresponding cross power spectral densities with the previous and posterior neighboring stretches, as shown in the paper. From the analysis results the dynamic material properties are modified according to the equivalent linear approach. It should be mentioned that this procedure is a generalization of the equivalent nonlinear method where the whole input motion (one window) is considered. Needless to stress the fact that when the input motion is divided into several stretches (windows) the actual response approximation will be improved significantly. The accuracy of the procedure advanced here is then evaluated through comparisons with the widely recognized nonlinear computer code named NONSAP. The comparison of the results obtained with both methods show not only the accuracy of the advanced procedure but its much lower consuming time, making it quite appealing to be used in practice.