Abstract: In order to analysis the uncertain problems of dynamical characteristics of shrouded turbine blades accurately， an interval method for complex structures combined by interval theory and finite element method has been presented. The solution procedure for the interval dynamical characteristics is given based on the commercial finite element software. Taking the dispersion of operation temperature， contact status of the shrouds and angular stiffness of firtree root into account， the modal characteristics and vibration response of a shrouded turbine blade are studied， and as a consequence the effects of typical uncertain parameters of structures and loads on the vibration characteristics of blade are obtained. The results show that the computational efficiency can be improved more than 10 times， and the relative error of the calculated results is less than 50% compared with Monte Carlo method， in particular the results obtained by the interval method are more reliable. Moreover it is not necessary to get the information about the probability distribution characteristics for the uncertain parameters by this developed method， which indicates a better engineering application prospect compared to most probabilistic methods.

Key words: Blades；Uncertainty；Interval method；Finite element method；Dynamical characteristics

摘要： 为准确计算分析带冠涡轮叶片振动特性的非确定性问题，将区间组合法与有限元法相结合，发展了适用于复杂结构振动特性的区间求解方法，并建立了基于商用有限元软件的区间振动特性求解流程。考虑工况温度、叶冠接触状态和榫头约束角刚度的分散性，对带冠涡轮叶片的模态特性和振动响应进行了求解，研究得到了典型结构、载荷等非确定性参数对叶片振动特性的影响规律。研究结果表明，与蒙特卡洛法相比，该方法可使计算效率提高10倍以上，计算结果的相对误差不大于50%，获得振动特性的区间结果更为可靠，并且该方法无需对非确定性参数的概率分布进行假设，具有良好的工程应用前景。

关键词: 叶片；非确定性；区间方法；有限元法；振动特性