中文摘要：

采用Lagrange方程考虑6个方向的自由度，推导了考虑弯扭耦合振动的转子系统运动方程。分析了两种不平衡的作用，即静不平衡和动不平衡，同时考虑了重力和陀螺效应的影响。当外激励力和外激励力矩作用在该系统上时，采用数值仿真研究了系统弯扭耦合的非线性振动特性，发现系统所具有的各种非线性振动现象。对于建立比较完备的转子弯扭耦合振动模型和转子系统的故障诊断具有一定的意义。

英文摘要：

The coupled torsional-lateral model of the rotor system is set up and governing equations are derived using Lagrange approach with six degrees of freedom. Two kinds of unbalances including static unbalance and dynamic unbalance are imposed on the rotor system. The gyroscopic effect and the gravity are included. When the external force and the external moment act on the system, numerical simulation method is utilized to investigate the nonlinear dynamics of the coupled torsional-lateral vibration of the unbalanced rotor system, and many nonlinear vibration phenomena are found. This work is meaningful for setting up a complete coupled torsional-lateral model of the rotor system and helpful for the diagnosis of rotor faults.