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

doi:10.6052/0459-1879-2012-2-20120228

Abstract

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

CLC Number:

O322
O324

Zhang Lei, Wu Yongjun. FIRST-PASSAGE OF COUPLED DUFFING-VAN DER POL SYSTEM IN THE CASE OF EXTERNAL RESONANCE[J]. Chinese Journal of Theoretical and Applied Mechani, 2012, 44(2): 437-446.

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