In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achiev...In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact to the relative magnitude of the two feedback gains. the condition of the well-matched feedback gains. control strategy of time-delayed feedback.展开更多
研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内...研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定。典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线。展开更多
基金Project supported by National Natural Science Foundation of China(No.51265010)Graduate Special Innovation Funds for East China Jiaotong University(No.YC2013-X007)
基金supported by the National Natural Science Foundation of China(11172226)
文摘In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact to the relative magnitude of the two feedback gains. the condition of the well-matched feedback gains. control strategy of time-delayed feedback.
文摘研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定。典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线。
