中文摘要：

以混流式水轮机为研究对象,应用有限单元法建立转轮叶片的动力学方程,根据转轮叶片的频率方程计算转轮叶片的固有频率,依据水流激励频率与转轮叶片固有频率之差在规定范围内的关系准则,推导转轮叶片的共振失效概率和可靠度的计算公式,并通过实例对混流式水轮机转轮叶片的频率可靠性进行分析。

英文摘要：

Taking the Francis turbine as an object of study,the dynamic equations of the runner blade are established by the finite element method.Based on the frequency equations,the natural frequencies of the runner blade are obtained.According to the criterion that the difference between the natural frequencies and driving frequencies should be less than specific values,the formulae are derived,by which the resonant failure probability and the reliability of the runner blades are respetively calculated.Finally,the frequency reliability of the runner blades of Francis turbine is analyzed by an example.