多支承转子系统辛空间传递矩阵法及应用

摘要

Based on the variational principle,dual variables were introduced,and the multi-support rotor system was imported into symplectic space.The symplectic transfer matrix in the symplectic space was presented for the rotor system,which reflects the symplectic conservation property.A model of the rotor system was built.MATLAB was used to analyze the model.The natural frequency and other modal parameters were obtained.The calculated values are consistent with the values obtained by the finite element method.The effectiveness of the method was confirmed by comparing the results with traditional methods.After large amount of calculations the critical speeds were obtained.The relationship between the critical speeds and the support stiffness was studied.This work provides reference for the optimization of rotor systems.%由变分原理出发,引入对偶变量,将多支承转子系统导入辛体系,推导出转子系统在辛空间中的传递辛矩阵格式,体现了保辛的性质.建立多支承转子系统模型,运用MATLAB对模型进行计算分析,求得固有频率等模态参数,计算结果与有限元方法计算值相吻合.通过与传统方法的计算结果比较证明了该计算方法的有效性.求解得到转子系统各阶临界转速,探讨了支承刚度的改变对转子各阶临界转速的影响,为多支承转子系统的优化设计提供了依据参考.