裂纹转子弯扭耦合振动非线性特性分析

以非线性涡动影响下的水平Jeffcott裂纹转子为研究对象，分别建立了刚性支承的纯弯曲振动、弯扭耦合振动和轴承支承的弯扭耦合振动三种运动微分方程，针对三种模型，分析了裂纹转子系统响应的分叉与混沌特性。数值计算结果表明： 较大时，三种模型下的弯振分叉图均呈现出复杂的非线性特性，尤其在 附近，各种周期、拟周期和混沌响应交替出现，阵发性特点非常明显，系统由拟周期路径通向混沌。模型1、2的弯振分叉图特性基本相似，模型3则具有更为复杂的非线性特性。模型2、3的扭振分叉图与各自的弯振分叉图极为相似，且非线性特性也基本相同。分析结果有助于更充分了解裂纹转子的动力学特性。

Nonlinear analysis on coupled flexural and torsional vibrations of cracked rotor

A Jeffcott cracked rotor considering nonlinear influences of whirl speed was investigated.Three kinds of nonlinear dynamical models were established seperately,which are pure flexural vibration model of rigidly supported beam,coupled flexural and torsional vibrations model of beam supported on rigid base and coupled flexural and torsional vibrations model of beam supported on elastic bearings.The behaviors of bifurcation and chaos were analyzed.Numerical simulations demonstrate that a complex nonlinear phenomenon is presented on the bifurcation plots of flexural vibrations of three kinds of models when the flexural stiffness difference Δkη is fairly large.Periodic,quasi-periodic and chaotic motions appear alternately when the rotating speed is near to 2/3ωc.The bifurcation plot of flexural vibration of model 1 is similar to that of model 2.And model 3 has more complex nonlinear characteristic.The bifurcation plots of torsional vibration of model 2 and 3 are similar to those of flexural vibration.And their nonlinear characteristics are all the same too.The analyzed results are helpful to knowing more about the dynamic characteristics of cracked rotors.