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First-Passage Time of Duffing Oscillator under Combined Harmonic and White-Noise Excitations

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Abstract

The first-passage time of Duffing oscillator under combined harmonic andwhite-noise excitations is studied. The equation of motion of the system is firstreduced to a set of averaged Itô stochastic differential equations by using thestochastic averaging method. Then, a backward Kolmogorov equation governing theconditional reliability function and a set of generalized Pontryagin equationsgoverning the conditional moments of first-passage time are established. Finally, theconditional reliability function, and the conditional probability density and momentsof first-passage time are obtained by solving the backward Kolmogorov equation andgeneralized Pontryagin equations with suitable initial and boundary conditions.Numerical results for two resonant cases with several sets of parameter values areobtained and the analytical results are verified by using those from digital simulation.

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Authors and Affiliations

  1. Department of Mechanics, Zhejiang University, Hangzhou, 310027, P. R. China

    W. Q. Zhu & Y. J. Wu

  2. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100008, P. R. China

    W. Q. Zhu & Y. J. Wu

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  1. W. Q. Zhu
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  2. Y. J. Wu
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Zhu, W.Q., Wu, Y.J. First-Passage Time of Duffing Oscillator under Combined Harmonic and White-Noise Excitations. Nonlinear Dynamics 32, 291–305 (2003). https://doi.org/10.1023/A:1024414020813

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  • DOI: https://doi.org/10.1023/A:1024414020813

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