变截面旋转叶片的非线性动力学研究
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国家自然科学基金(11427801,11290152,11572006)


Nonlinear dynamics analysis of rotating blade with varying cross⁃section
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    摘要:

    将航空发动机叶片简化成变截面旋转悬臂板进行动力学分析.叶片在气动力下变速旋转,其气动载荷用一阶活塞理论表示,同时考虑了叶片的预扭转角?预安装角以及叶片承受的巨大离心力.叶片的非线性位移关系由Vonkarman 大变形理论得出,利用Hamilton 原理建立非线性动力学方程.对所得方程进行Galerkin离散,将偏微分方程转化为常微分方程.考虑1∶3的内共振关系,利用渐近摄动法进行摄动分析,得到四维直角坐标形式下的平均方程.最后对平均方程进行数值模拟,研究了扰动转速对系统非线性动力学行为的影响,得到了不同转速情况下的相图?波形图以及频谱图.结果表明:随着扰动转速的变化,叶片存在倍周期?概周期和混沌等非线性动力学行为.

    Abstract:

    In this study, the aero?engine blade is modeled as a cantilever rotating plate with varying cross?section. The blade rotates at a varying speed under the aerodynamic load expressed by the first?order piston theory. At the same time, the pre?setting angle, pre?twist angle and centrifugal force are taken into consideration. The Von Karman plate theory is then applied to derive the nonlinear displacement?strain relationships, and Hamilton′s principle is applied to derive the nonlinear partial differential governing equations of motion.Additionally, the Galerkin method is employed to deduce the partial differential equation into two nonlinear ordinary differential equations. Considering the case of 1 ∶3 internal resonance, the asymptotic perturbation method is used to obtain a four?dimensional nonlinear averaged equation. The numerical method is also used to find the nonlinear dynamic responses of the blade. It is found that the disturbance rotating speed has an important influence on its nonlinear behavior. The frequency spectrum phase, phase portrait, and waveform phase are all presented. It is observed that the blade exhibits the nonlinear dynamics behavior, such as the chaotic, periodic motions and quasi?periodic motions due to the influence of disturbance rotating speeds.

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张伟,袁双,郭翔鹰.变截面旋转叶片的非线性动力学研究[J].动力学与控制学报,2018,16(4):309~316; Zhang Wei, Yuan Shuang, Guo Xiangying. Nonlinear dynamics analysis of rotating blade with varying cross⁃section[J]. Journal of Dynamics and Control,2018,16(4):309-316.

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  • 收稿日期:2017-01-10
  • 最后修改日期:2017-05-02
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  • 在线发布日期: 2018-06-27
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