Responses of discretized systems under narrow band nonstationary random excitations. Part 2: nonlinear problems

In a companion paper, the extended stochastic central difference (ESCD) method was presented for computation of responses of linear multi-degrees-of-freedom (mdof) systems under narrow band stationary and nonstationary random excitations. The present paper is concerned with the generalization of the ESCD method for computation of nonlinear mdof systems. The generalization is based on a combination of the ESCD method with statistical linearization (SL) technique, modified adaptive time scheme (ATS), and time coordinate transformation (TCT). Unlike the conventional SL technique, the generalized ESCD method is applicable to mdof systems with large nonlinearities. Comparison is made of the computed results applying the generalized ESCD method to those obtained by the Monte Carlo simulation (MCS). Excellent agreements were obtained. It was observed that the proposed method is very efficient compared with the MCS.