FIRST-PASSAGE OF COUPLED DUFFING-VAN DER POL SYSTEM IN THE CASE OF EXTERNAL RESONANCE

First-passage failure of two-DOF Duffing-van der Pol system with strong nonlinearity under combined harmonic and wide-band stochastic excitations was studied. In the case of external resonance, the equations of motion of the system are reduced to a set of averaged It\^o stochastic differential equations after stochastic averaging. Then, the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are established. Under specified boundary and initial conditions, the method of finite difference is used to solve the high-dimensional backward Kolmogorov equation and Pontryagin equation to yield the conditional reliability function, the mean first-passage time and the conditional probability density function of the mean first-passage time. Different parameters are chosen to show the influence on the reliability and mean first-passage time of the original system. All theoretical results are verified by Monte Carlo simulation.