Probabilistic solutions of nonlinear oscillators to subject random colored noise excitations

Abstract

Random colored noise excitations, more close to real environmental excitations, are considered. In this paper, probabilistic solutions of nonlinear SDOF systems excited by colored noise are analyzed. With the aid of filtering method, the initial equation of motion is transferred to four coupled first-order SDEs. As a result, a Markov process of enlarged system responses comes into being, and traditional FPK equation method can be employed. However, this way makes the corresponding FPK equation become four-dimensional. In order to solve this problem, the developed and improved exponential polynomial closure (EPC) method is employed. In the solution procedure, an approximate exponential function is extended to include four state variables. Then additional unknown coefficients associated with extended state variables are produced, and the solution procedure becomes more complicated. On the other hand, since there is no exact solution, Monte Carlo simulation (MCS) is performed to verify the efficiency of the developed EPC method. Four examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Numerical results show that the developed EPC method provides good agreement with the MCS method. Moreover, the effect of bandwidth for colored noise on system responses is taken into account.