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中文摘要：
研究叶片与转子-轴承系统的耦合非线性振动，建立了一个带叶片的双盘转子-轴承系统的非线性动力学模型，其中包含一个弹性转轴、两个滑动轴承、两个刚性圆盘和两组弹性叶片。为了分析叶片的惯性影响，将其简化为单摆模型。采用4阶Runge-Kutta法进行了数值模拟，并利用分岔图、三维谱图、轴心轨迹和Poincare映射图等方法分析了系统的非线性动力学特性。研究发现，随着转速的变化，系统响应演化出了倍周期运动、概周期运动、混沌运动和倍周期分岔等典型的非线性动力学行为。在与忽略了叶片振动的转子系统对比后发现，叶片振动使转子发生混沌运动的转速区域增大。在某些参数条件下，采用不同的叶片刚度，叶片振动可能引起转子系统产生混沌运动。
英文摘要：
A nonlinear dynamical model of a double disk rotor-bearing system with an array of blades, including a flexible shaft, two journal bearings, two rigid disks and two arrays of elastic blades, was established to investigate the couple vibration between the rotor and blades. The blade was modeled as a pendulum to emphasize the inertia effect. Through Runge-Kutta numerical calculation, the nonlinear dynamical behavior of couple system was analyzed with the help of bifurcation diagram, three dimensional spectrum plot, whirl orbit and Poincare map etc. It shows that there exist the typical nonlinear dynamical behavior in the response of couple system, such as period-n, quasi-period, chaos and double periodic bifurcation. Comparing with the behavior of the system in which the effect of the blades vibration is neglected, the vibration of blades causes the rotating speed interval where the chaos occurs to increase. Under certain operation condition, when the certain stiffness of blade is employed, the vibration of blades can cause the occruance of chaos in the response of the rotor.
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Second-order approximation of primary resonance of a disk-type piezoelectric stator for traveling wa
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