Dynamical reliability of internally resonant structural system under Gaussian white noise excitations

Theoretically, the dynamical reliability of internally resonant structural system with Many-Degrees-of-Freedom (MDOF) under Gaussian white noise excitations is studied. By using stochastic averaging method, the equations of motion of the original system are reduced to a set of averaged Ito 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. All results are verified by Monte Carlo simulation.