Abstract
In this paper, transient influence of correlation between external and parametric excitations on system response is investigated. Time variable has been taken into account. This does not seem to have been studied previously. By describing correlation between excitations quantitively with correlated coefficient, general Fokker-Planck-Kolmogorov (FPK) equation is reformulated with two parts. The first part relates to the one of independent excitations, while the other part is caused by the correlated excitations. Then, exponential polynomial closure (EPC) method, by taking time variable into account, is further developed for transient responses of nonlinear oscillators under correlated excitations. With the improved EPC method, typical system of Duffing oscillator under correlated external and parametric Gaussian white noise excitations is investigated. Based on the results, it is found the influence of correlation between excitations on system response depends directly on the magnitude and the sign of the correlation coefficient. Besides, the influence seems stationary, and not affected by the time. In addition, the results obtained from the EQL method are not consistent with the actual ones with unsymmetrical PDFs and nonzero means. It is indicated that the EQL method is not applicable to such case.
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