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采用多级模态综合技术并利用结构旋转对称的特点，建立包括转动部件和固定部件在内的水轮机整机系统动力特性分析模型。考虑到油膜特性引起的矩阵不对称性是局部的，将实模态分析与复模态分析结合，仅需对极小规模的非对称矩阵解左右复特征值问题。给出的轴—板架系统复特征值结果与整体计算结果吻合，而计算时间大为节省。大型水轮机包括主轴、顶盖、下机架和上机架的整机系统的动力特性算例中，不仅得到了主轴弯曲振动频率，而且得到了固定部件与主轴耦合振动的频率和振型。算例表明了本文模型不仅理论先进，而且能用于工程实际计算。
Using the multi-level modal synthesis technology and utilizing the characteristics of rotational symmetry of the structure, the dynamic characteristic analysis model of the complete hydraulic turbine system including the rotating components and the fixed components is established. Considering that the matrix asymmetry caused by the oil film properties is local, combining the real modal analysis with the complex modal analysis, it is only necessary to solve the complex eigenvalue problems for the asymmetric matrix of very small scale. The results of the complex eigenvalue of the shaft-plate system coincide with the overall calculation results, and the calculation time is greatly saved. The dynamic characteristics of the whole system including the main shaft, the top cover, the lower frame and the upper frame of the large hydraulic turbine are not only obtained the frequency of the bending vibration of the main shaft, but also the frequency and mode of the vibration of the fixed part and the main shaft are obtained. The example shows that this model not only has advanced theory, but also can be used in actual engineering calculation.