基于高保真有限元模型失谐叶盘受迫响应的统计特性

采用极值理论分析失谐叶盘最大受迫响应的统计特性并应用于某压气机叶盘上。对失谐叶盘进行减缩建模，运用蒙特卡洛方法模拟响应计算，研究不同激励阶次下最大响应放大因子的分布特性。采用极值理论对最大响应放大因子分布进行统计学建模，以极大似然估计方法求解未知参数，进行分布拟合，并采用K-S(Kolmogorov-Smirnov)检验方法检验各分布函数拟合的好坏程度。对某压气机叶盘进行失谐响应统计特性分析，对比了7种分布函数对最大响应放大因子的拟合效果，结果表明:极值分布、二参数威布尔分布、正态分布、对数正态分布和伽马分布拟合效果较差；常用的三参数威布尔分布不如广义极值分布的拟合效果好。因此，说明广义极值分布更能准确地描述失谐叶盘动力响应的统计特性。 

Statistical characteristics of forced response in mistuned bladed disks based on high-fidelity finite element model

The extreme value theory was used to analyze the statistical characteristics of maximum forced response of the mistuned bladed disks, and applied to a compressor disk. The mistuning bladed disk was reduced and modeled. The Monte Carlo method was used to simulate the response calculation, and the distribution characteristics for the amplification factor of the maximum response under different engine order excitations were studied. The extreme value theory was used to model the maximum response distribution, and the maximum likelihood estimation method was introduced to get the unknown parameters. The K-S(Kolmogorov-Smirnov) test was employed to test the goodness of fit of different distribution functions. The statistical characteristics of the response of a compressor disk were analyzed. The fitting results of seven kinds of distribution functions for the amplification factor of the maximum response were compared. Results showed that the fitting effects of the extreme value distribution, two-parameter Weibull distribution, normal distribution, lognormal distribution and Gamma distribution were all poor; the fitting effect of the commonly used three-parameter Weibull distribution was not as good as that of the generalized extreme value distribution. Therefore, the generalized extreme value distribution can more accurately describe the statistical characteristics of the dynamic response of mistuned bladed disks.