First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

The first passage failure of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations in the case of external resonance is studied. First, a stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations using generalized harmonic functions is reviewed briefly. Then, a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established from the averaged It equations, respectively. The conditional reliability function, and the conditional probability density and conditional mean of the first passage time are obtained from solving these equations together with suitable initial condition and boundary conditions. The comparison between the analytical results and those from Monte Carlo simulation for an example shows that the proposed method works very well. It is also shown by using Monte Carlo simulation that the reliability of the system in the case of external resonance is much lower than that in the non-resonant case.