First-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations

• Internal resonance is theoretically studied in MDOF quasi-integrable Hamiltonian systems.
• The stochastic excitation is modeled as wide-band stochastic noise, not Gaussian white noise.
• High-dimensional partial differential equations are solved.

In this paper, first-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitations is studied theoretically. By using stochastic averaging method, the equations of motion of the original internally resonant Hamiltonian system are reduced to a set of averaged Itô stochastic differential equations. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are established under appropriate boundary and (or) initial conditions. An example is given to show the accuracy of the theoretical method. Numerical solutions of high-dimensional backward Kolmogorov and Pontryagin equation are obtained by finite difference. All theoretical results are verified by Monte Carlo simulation.