First-passage problem of strongly nonlinear stochastic oscillators with external and internal resonances

The first-passage problem of 2-DOF strongly nonlinear oscillators subject to combined harmonic and wide-band stochastic excitations is studied in this paper. The equations of motion of the original system are reduced to a set of averaged Itô stochastic differential equations in the case of both external and internal resonances. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean first-passage time are established. The conditional reliability function, mean first-passage time and the conditional probability density of the mean first-passage time are obtained by solving the backward Kolmogorov equation and Pontryagin equation under suitable initial and boundary conditions. All theoretical results are verified by Monte Carlo digital simulation.