First passage failure of SDOF nonlinear oscillator with lightly fractional derivative damping under real noise excitations |
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Authors: | Lincong ChenWeiqiu Zhu |
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Affiliation: | a College of Civil Engineering, Huaqiao University, 361021, Xiamen, Chinab Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China |
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Abstract: | The first passage failure of single-degree-of-freedom (SDOF) nonlinear oscillator with lightly fractional derivative damping under real noise excitations is investigated in this paper. First, the system state is approximately represented by one-dimensional time-homogeneous diffusive Markov process of amplitude through stochastic averaging. Then, the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established from the averaged Itô equation for Hamiltonian. The conditional reliability function, the conditional probability density and mean of the first passage time are obtained by solving these equations together with suitable initial condition and boundary conditions. Finally, two examples are worked out in detail and the analytical solutions are checked by those from the Monte Carlo simulation of original systems. |
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Keywords: | First passage failure Fractional derivative Stochastic averaging Real noise |
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