Chinese Journal of Theoretical and Applied Mechani ›› 2012, Vol. 44 ›› Issue (2): 437-446.DOI: 10.6052/0459-1879-2012-2-20120228

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

Zhang Lei, Wu Yongjun   

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2011-07-01 Revised:2011-07-23 Online:2012-03-23 Published:2012-03-23
  • Supported by:
    The project was supported by the National Natural Science Foundation of China (11132007, 10802030) and the Specialized Research Fund for Doctoral Program of Higher Education of China (200802511005).

Abstract: 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.

Key words: first-passage|stochastic averaging|backward Kolmogorov equation|Pontryagin equation|digital simulation

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