Reduction of response and first excursion probability for random excitation using nonlinear characteristics

Structures subjected to dynamic load have nonlinear characteristics in nature. Dynamic loads are sometimes random. In such a case, reliability of important structures is evaluated in probabilistic manner. First excursion failure is one of the most important failure modes of the structure. In this paper, methods for obtaining the response and the first excursion probability of the structure with nonlinear characteristic subjected to random dynamic load are presented. For simplicity, single-degree-of-freedom system is used as analytical model. Two-degree-of-freedom system is also used in order to examine coupling effect of two systems. Hysteresis loop characteristic caused by plastic deformation is considered. The mean square value of the response and the first excursion probability are obtained. It is concluded that the response and the first excursion probability are reduced by considering the hysteresis loop characteristic caused by plastic deformation.