Journal
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
Volume 54, Issue 8, Pages 1999-2006Publisher
SCIENCE PRESS
DOI: 10.1007/s11431-011-4474-1
Keywords
first-passage; stochastic averaging method; generalized harmonic function; Kummer function; Galerkin method
Funding
- National Natural Science Foundation of China [11025211]
- Natural Science Foundation of Zhejiang Province [26090125]
- Special Fund for National Excellent PhD Dissertation
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First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged Ito stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.
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