Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing-Rayleigh-Mathieu system

• 来源期刊: 力学学报(英文版)
• 年，卷（期）: 2008,（5）
• 页码范围: 575-582
• 页数: 8页
• 语种: 英文
• DOI: 10.1007/s10409-008-0140-7

摘要

The first-passage statistics of Duffing-Rayleigh-Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the correspon-ding backward Kolmogorov equation and Pontryagin equa-tion are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.