Non-Linear Stochastic Response Of Structures With Bilinear Hysteretic Elements To White Noise Excitation

The analysis of the dynamic behavior of structures under earthquake excitations is deeply complex problem due to several factors, namely; the unpredictability of the earthquake source, which corresponds to a fault rupture associated with an enormous release of vibratory energy in some parts of the earth crust, the complexity of the seismic wave propagation and the uncertainties related either to the local conditions or to the properties of the structures. The high level of difficulty of this problem is still considerably increased when we take into account that the real structures should not be modeled as linear systems, but as non-linear hysteretic systems and the randomness of the excitation is considered. In this paper, the equivalent linearization technique is presented and applied to obtain the stationary response of non-linear structures containing bilinear hysteretic elements when subjected to white noise excitation. The Root Mean Square responses are easily obtained. The space state formulation is used, and thus, the differential model representing the bilinear elements is easily implemented in the analysis. The excitation is modeled as white noise random process. The results showed the importance of equivalent linearization technique, and its easy application to structures