计算多转子系统临界转速的整体传递矩阵法

提出了整体传递矩阵法中耦合单元的概念，导出了各向同性和各向异性耦合单元的传递矩阵，并给出了几个算例。整体传递矩阵法是取各转子状态向量的集合作为系统的状态向量，各转子同时对系统状态向量进行传递，求得多转子轴系的整体传递矩阵方程，代入整体边界条件进行求即可得到多转子轴系的临界速。与子结构传递矩阵法相比，整体传递矩阵法不必将多转子系统在耦合单元处分割开来，示引入未知内力和位移，也不必建立分割处的平衡方程或变形协调条件。

A whole transfer matrix method for calculating the critical speed of multi-rotor system

The concept of coupling element in whole transfer matrix method is proposed, the transfer matrix of isotropic coupling element and that of anisotropic coupling element are derived and some numerical examples are given in the paper. The whole transfer matrix method takes the set of state vectors of axes as the systematical state vector, and each rotor transfers the systematical state vector simultaneously to obtain the equations for whole transfer matrix method. Substituting the systematical boundary conditions into the equations of whole transfer matrix method and solving it, the critical speeds of multi-rotor system can be obtained. Comparing with sub-structure transfer matrix method, the whole transfer matrix method is more suitable for engineers because of that the multi-rotor system does not be divided at coupling places and it does not need to construct the balance equations or deformation compatibility equations.