外共振耦合Duffing-van der Pol系统的首次穿越

研究了谐和力与宽带噪声激励下二自由度强非线性Duffing-van derPol系统的首次穿越问题. 在外共振情形, 应用随机平均法将系统动力学方程化为关于振幅与角变量的Itô随机微分方程. 然后建立了系统的可靠性函数满足的后向Kolmogorov方程以及平均首次穿越时间满足的Pontryagin方程. 在一定的边界条件和初始条件下, 用有限差分法求解了这两个高维偏微分方程, 得到系统的条件可靠性函数、平均首次穿越时间以及平均首次穿越时间的条件概率密度. 讨论了不同参数对系统可靠性以及平均首次穿越时间的影响. 用Monte Carlo数值模拟验证了理论方法的有效性.

FIRST-PASSAGE OF COUPLED DUFFING-VAN DER POL SYSTEM IN THE CASE OF EXTERNAL RESONANCE

First-passage failure of two-DOF Duffing-van der Pol system with strong nonlinearity under combined harmonic and wide-band stochastic excitations was studied.In the case of external resonance,the equations of motion of the system are reduced to a set of averaged ltd stochastic differential equations after stochastic averaging.Then,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are established.Under specified boundary and initial conditions,the method of finite difference is used to solve the high-dimensional backward Kolmogorov equation and Pontryagin equation to yield the conditional reliability function,the mean first-passage time and the conditional probabiUty density function of the mean first-passage time.Different parameters are chosen to show the influence on the reliability and mean first-passage time of the original system.All theoretical results are verified by Monte Carlo simulation.