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The first passage failure of SDOF strongly nonlinear stochastic system with fractional derivative damping. (English) Zbl 1173.93031

Summary: The first passage failure of Single-Degree-Of-Freedom (SDOF) strongly nonlinear stochastic system with fractional derivative damping is studied. The stochastic averaging method for SDOF strongly nonlinear stochastic systems with fractional derivative damping under white noise excitations using the generalized harmonic function is introduced. The averaged Itô equation for Hamiltonian is obtained by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the mean of the first passage time are established. The conditional reliability function, and the conditional probability density and mean first passage time are obtained from solving these equations together with a suitable initial condition and suitable boundary conditions. Finally, two examples are worked out in detail. The solutions are confirmed by using Monte Carlo simulation of original systems.

MSC:

93E03 Stochastic systems in control theory (general)
70L05 Random vibrations in mechanics of particles and systems
70Q05 Control of mechanical systems
93C10 Nonlinear systems in control theory
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