Systematic analysis of the concept of equivalent linear behavior in seismic engineering

In seismic engineering, taking into account the non-linear behavior of the structure into the calculation of its responses against strong ground motions, which are due to plastic and/or damage, is not easy because of the need, in terms of computation time and memory, due to many iterations required at each step in order to satisfy the equilibrium. It is common that many concepts of equivalent linear behavior have been used in order to determine the maximal response of structure without performing non-linear transient calculation. In this paper, we deal with systematic and argumentative analysis in order to establish a concept of equivalent linearization by considering the equivalence criterion through the transfer function from the time domain to the frequency domain. Its idea is to identify the frequency and damping of the equivalent linear oscillator whose theoretical transfer function of response in acceleration fits the best the experimental one of the nonlinear system. This concept will be applied to elastoplastic Sdof oscillators undergoing the filtered white noise signal Clough-Penzien. As the result, this equivalent linearization reestablishes the transferred signal through a structure with the non-linearity.