Abstract
First-passage failure of strongly nonlinear oscillators under combined harmonic and real noise excitations is studied. The motion equation of the system is reduced to a set of averaged Itô stochastic differential equations by stochastic averaging in the case of resonance. Then, the backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function and the conditional probability density and mean first-passage time are obtained by solving the backward Kolmogorov equation and Pontryagin equation with suitable initial and boundary conditions. The procedure is applied to Duffing–van der Pol system in resonant case and the analytical results are verified by Monte Carlo simulation.
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Wu, Y.J., Luo, M. & Zhu, W.Q. First-passage failure of strongly nonlinear oscillators under combined harmonic and real noise excitations. Arch Appl Mech 78, 501–515 (2008). https://doi.org/10.1007/s00419-007-0174-5
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DOI: https://doi.org/10.1007/s00419-007-0174-5