非线性时变结构时变动力可靠性分析的FPK法

The FPK Method on Time-varying Dynamic Reliability of Nonlinear Time-varying Structure\+*

本文研究了一类多自由度非线性时变结构的振动模型，用ＦＰＫ法得出了体系的位移与速度响应的平稳联合概率密度函数的解析解，提出了基于Ｐｏｓｓｉｏｎ 假设的时变动力可靠性的一整套计算公式；作为例子，给出了任意非线性刚度的单自由度时变结构时变动力可靠性的解析解，并将其特例情况－ Ｄｕｆｆｉｎｇ 体系的动力响应和超越率结果与现有理论解作了比较；本文方法对结构维护与评估有广泛应用价值。

In this paper,the vibration model of a class of nonlinear time-varying structure of multi-degrees of freedom is studied,and the exact solution of stationary joint probability density function for the displacement and velocity response of system is deduced by Fokker-Plank method A complete set of calculating formula of time-varying dynamic reliability based on possion hypothesis is proposed;As an example,the exact solution of time-varying dynamic reliability for time-varying structure of single degree of freedom with arbitrary nonlinear rigidity is given The dynamic response and passage rate of Duffing system which is its special case are compared with the existed theoretical solutions;The method of this paper is of extensive applied value \ \