Abstract Vibration modes with repeated eigenvalues often occur in engineering design and analysis practices due to geometrical symmetries of structural systems such as the cyclic symmetry of bladed disk assemblies of turbomachinery. However, the degeneration of eigenvector space and the resulting discontinuities have prevented useful applications of eigensensitivities to vibration analysis of a wide class of problems with repeated modes. To overcome such difficulties, a new concept of a global design variable is developed in which all intended multivariate design modifications are grouped into a single global design variable. Eigensensitivities have then been formulated for repeated eigenvalues from which accurate predictions of vibration characteristics can be made. Further, second order eigenvalue derivatives are also employed to further improve the accuracy of predicted vibration properties. Such newly formulated eigensensitivity analysis has been effectively applied for the first time to the prediction of mistuning effect of bladed disk assemblies. Numerical results from a realistic discrete parameter model of a bladed disk have demonstrated that not only natural frequencies and mode shapes can be predicted very accurately, but also blade vibration responses under engine order excitations. In addition, the proposed eigensensitivty analysis can predict the statistical variations of blade vibrations under random mistuning. Finite element modeling and vibration testing of a practical bladed disk structure have been carried out to demonstrate the practical potential of the proposed method to be possibly integrated into finite element analysis for structural modification predictions, especially for structures with repeated eigenvalues such as bladed disks.

中文翻译：

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使用本征敏感性分析预测叶片盘的失谐效应

摘要 由于结构系统的几何对称性，如涡轮机械叶盘组件的循环对称性，在工程设计和分析实践中经常出现具有重复特征值的振动模式。然而，特征向量空间的退化和由此产生的不连续性阻碍了特征敏感性在具有重复模式的广泛类别问题的振动分析中的有用应用。为了克服这些困难，开发了全局设计变量的新概念，其中所有预期的多变量设计修改被分组到单个全局设计变量中。然后为重复的特征值制定了特征灵敏度，从中可以准确预测振动特性。更多，二阶特征值导数也被用来进一步提高预测振动特性的准确性。这种新制定的特征灵敏度分析首次有效地应用于叶片盘组件失谐效应的预测。叶片盘的真实离散参数模型的数值结果表明，不仅可以非常准确地预测固有频率和振型，而且可以非常准确地预测发动机阶次激励下的叶片振动响应。此外，所提出的特征敏感性分析可以预测随机失谐下叶片振动的统计变化。