The stochastic Newmark algorithm for random analysis of multi-degree-of-freedom nonlinear system

摘要

Based on deterministic Newmark integration formulation, a stochastic Newmark algorithm (SNA) is proposed and developed in this paper. A one-step recursive expression is derived to calculate the covariance matrix response of nonlinear systems subjected to non-stationary random disturbances. The autoregressive moving average (ARMA) algorithm is used for simulating realizations of nonwhite random excitation. Closed form parameters of (ARMA) model are given for a class of random process possessing rational spectral density. This method is illustrated by calculating the mean value and mean square response of systems with symmetric and asymmetrical nonlinearity. Numerical simulations are carried out to demonstrate the accuracy and effectiveness of the method.