Abstract
By using of Gegenbauer orthogonal polynomials，an effective numerical method for the reliability analysis of double random Duffing system with large coefficient of variation is presented. On the basis of the first passage model，the fourth-moment technique，the Edgeworth series approximation theory and the orthogonal polynomial expansion method are employed to develop a reliability analysis method systematically. The dynamic reliability and mean reliability of the system is discussed. The results obtained by this method are verified by Monte-Carlo simulations.
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