Chinese Journal of Theoretical and Applied Mechani ›› 2015, Vol. 47 ›› Issue (5): 807-813.DOI: 10.6052/0459-1879-15-058

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THE INFLUENCE OF ONE-TO-ONE INTERNAL RESONANCE ON RELIABILITY OF RANDOM VIBRATION SYSTEM

Wang Haoyu, Wu Yongjun   

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2015-02-11 Revised:2015-07-08 Online:2015-09-23 Published:2015-07-21
  • Supported by:

    The project was supported by the National Natural Science Foundation of China (11272201, 11372271, 11132007).

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 Itô 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 Itô 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.

Key words:

1:1 internal resonance|averaging method|reliability function|mean first-passage time|digital simulation

CLC Number: