随机约束汽轮机叶片频率的有限元分析

Finite Element Analysis for Frequency of Blade With Random Restriction

叶片连接状态存在不确定性。基于随机有限元方法,提出了一种随机约束弹性单元用于研究随机约束叶片频率的概率特征,此单元可以模拟自由叶片或成组叶片连接状态的不确定性对叶片频率的影响。推导出了约束刚度随机时的叶片振动特征值方程、频率的均值、频率对约束刚度系数的灵敏度矩阵、频率协方差矩阵、变异系数公式。频率均值表示叶片频率的平均水平,变异系数反映叶片频率的分散程度。通过实例研究了根部约束刚度的随机性对叶片频率的影响。

The connect status of the blade often exhibits uncertainty. A probabilistic analysis method was developed for frequencies analysis of turbine blade with random boundary condition based on stochastic finite element method. A random elastic restriction element was proposed to simulate the uncertainty in contact status of the free or ganged blades. The eigenvalues equations of the rotating blade with uncertain boundary condition are derived. The mean value, the sensitivity matrix, the covariance matrix and the coefficient of variance for the natural frequencies were given. The coefficient of variance can represent the degree of dispersion for the natural frequencies, and the mean value can represent the average level for the natural frequencies. The effects of restriction rigidity randomness on the blade natural frequencies are investigated through an example.