随机激励下高维包装振动系统的可靠性分析

研究了两自由度包装振动系统在受高斯白噪声外激励下的可靠性.利用由随机平均法导出的关于系统的独立运动积分的随机平均方程,通过系统本身的特性以及对漂移与扩散系数作出的一些假定,给出了系统的可靠性函数以及首通损坏的条件转移概率密度函数所满足的后向柯尔莫哥洛夫方程和福克-普朗克方程,并进一步详细地讨论了其边界与可解性条件.数值结果表明,关于系统的可靠性函数以及首通损坏的条件转移概率密度函数方面的结果是比较合理的,这也表明文中的分析方法是正确的.

Reliability of a High-dimensional Packaging Oscillatory System under Stochastic Excitation

The reliability of a packaging oscillatory system with two degree-of-freedom was investigated when the system was excited by Gaussian white noises. Firstly, the average equation about the system's energy was given based on the stochastic averaging method. Secondly, the system's safe region was defined, on which the boundary conditions were studied in detail under some suppositions on the drift and diffusion coefficients, and then, the corresponding BK and FPK equations were established to study the system's conditional reliability function and conditional transition probability density function. Numerical results about the conditional reliability function and conditional transition probability density function were also given to show that the theoretical analysis were reasonable, and the boundary conditions given in the present paper for the study on high dimensional BK equations were instructive.