中文摘要：

转子存在偏心距时,弯曲振动和扭转振动之间会相互作用产生弯扭耦合振动.目前对弯扭耦合振动的研究主要集中于其非线性特征,针对共振振幅大小和共振影响因素等共振特征的研究却比较少见.在实际的结构设计工作中,有时要利用耦合共振获取更大的振幅和振动能量.所以有必要从共振特征入手,对转子的弯扭耦合振动开展进一步的研究.首先建立偏心转子的弯扭耦合振动模型,使用小参数法对振动方程求解.其次分析扭转振动、弯扭振动产生耦合共振的条件,详细比较各振型共振振幅的大小和各参数对共振振幅的影响.然后以具体的算例,对各参数对弯扭耦合共振振幅大小的影响进行数值模拟,计算各阶共振振幅的大小,给出具有最大共振振幅时的参数条件,验证理论分析,为弯扭耦合振动的研究工作提供思路和依据.

英文摘要：

Eccentricity of rotors can induce bending-torsion coupled vibration of shafts. Currently, research of the bending-torsion coupling vibration is focused on the nonlinear characteristics, but seldom on the resonance characteristics of the bending-torsion coupled vibration of the shafts. In the structure design, bending-torsion coupled resonance vibration is sometimes employed to obtain larger amplitude and vibration energy. So, further study on the bending-torsion coupled vibration of rotors according to the resonance characteristics is necessary. In this paper, first of all, a model of an eccentric rotor for bending-torsion coupled vibration analysis was built, and the vibration equation was solved by small parameter method. Then, the condition of coupling resonance of the bending and torsional vibrations was analyzed. Finally, the theoretical analysis was demonstrated by numerical simulation. This work provides an idea and data base for the bending-torsion coupling vibration analysis.