根部约束为随机变量时汽轮机叶片静动频率概率分析

依据汽轮机叶片的实际工作情况，将汽轮机叶片根部约束简化为随机变量，该文提出了叶片静动频率的概率分析方法；应用能量法给出了叶根约束为随机变量时叶片振动频率的特征值方程；基于矩阵摄动分析技术推导小了叶片动静频率对叶片根部随机刚度的敏感度矩阵、叶片静动频率均值、协方差矩阵和变异系数（CCOV）公式，频率的变异系数从概率角度描述了频率的分散程度。最后通过实例研究根部约束刚度均值和变异系数对叶片静动频率的均值和变异系数的影响。

A PROBABILISTIC ANALYSIS FOR STATIC AND DYNAMIC FREQUENCY OF BLADE WITH UNCERTAIN RESTRICTION

A probabilistic analysis method is developed for frequencies analysis of turbine blade with uncertain restriction at the root of blade. An energy method is used to derive the eigenvalues equation of the rotating blade with uncertain root restriction. A matrix perturbation technique is employed for the probabilistic analysis to obtain the deterministic part of natural frequencies and vibration modes, the sensitivity matrix, the mean value, the covatiance matrix and the coefficient of variance (CCOV) for the nature frequencies. The coefficient of variance can represent the degree of dispersion for the nature frequencies, and the mean value and the variance can represent the probability distribution characters for the frequencies of blade. The effects of variations in the expectation and the variance of restriction rigidity on the expectation and the variance of the natural frequencies are investigated through an example.