A new approach for finding the design point of nonlinear systems under random excitation

Abstract

In order to perform nonlinear stochastic dynamic analyses, the tail equivalent linearization method may be employed, which entails the adoption of the first-order reliability method. The major computational challenge posed in this method is related to finding the design point excitation for the threshold corresponding to the failure of the nonlinear system. Furthermore, finding the design point is also a sufficiently challenging problem in some importance sampling techniques. In the present paper, a new approach for finding the design point of nonlinear SDOF systems under white noise excitation is introduced, one that is identical to the mirror image excitation method for a nonlinear elastic system and yields superior results for a nonlinear hysteresis system compared to the results of mirror image excitation method. It is then extended to filtered white noise excitations and multi degree of freedom systems. Some numerical examples are given for confirming the efficiency and accuracy of the proposed method by comparing it to other methods.