Abstract
Based on first-passage model, the reliability problem of two degrees-of-freedom random vibration system under Gaussian white noise excitations is studied analytically. In the case of 1:1 internal resonance, the equations of motion of the original system are reduced to a set of Ito stochastic differential equations after averaging. The backward Kolmogorov equation and the Pontryagin equation, which determine the conditional reliability function and the mean first-passage time of the random vibration systems, are constructed under appropriate boundary and (or) initial conditions, respectively. To study the influence of the internal resonance on the reliability, the averaged Ito stochastic differential equations, the backward Kolmogorov equation and the Pontryagin equation in the case of non-internal resonance are also derived. Numerical solutions of high-dimensional backward Kolmogorov equation and Pontryagin equation are obtained. The results of resonant case and non-resonant case are compared. It is shown that 1:1 internal resonance can greatly reduce the reliability. All the analytical results are validated by Monte Carlo digital simulation.
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