Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump

摘要

An approximate method for predicting the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump is proposed. By using the stochastic averaging method, the original system is reduced to one governed by a 1D averaged It? equation for the total energy with the Markov jump process as parameter. A Fokker-Planck-Kolmogorov (FPK) equation is then deduced, from which the approximate stationary probability density of the response of the original system is obtained for different jump rules. To illustrate the effectiveness of the proposed method, a stochastically excited Markov jump Duffing system is worked out in detail.