摘要
对简谐激励下陀螺系统的受迫振动及其在含时滞的位移和速度反馈控制下的动力学行为进行研究。利用拉格朗日方程,建立两自由度陀螺系统的运动微分方程。考虑主共振和1:1内共振的情况,采用平均法得到了平均方程。通过对平均方程进行化简,得到关于系统振幅的分岔方程,分别讨论各个参数对系统振幅的影响。根据奇异性理论,分析参数变化对系统分岔行为的影响。对受迫陀螺系统施加含时滞的位移和速度反馈控制,讨论反馈增益和时滞对系统振幅的影响。
The differential equations of motion with two degrees of freedom for a gyroscope system and its delayed feedback control were established based on the Lagrange equation. For the case of primary resonance and 1 ： 1 internal resonance, the averaging method was used to derive the averaged equations. Then according to the theory of singularity, the bifurcation equation, acquired from the averaged equations, was simplified to analyse the bifurcation behavior of the system. Finally, the effects of feedback parameters on the amplitude of forced vibration were discussed when the sysyem is acted by displacement and velocity feedback control with time delay.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第9期63-68,共6页
Journal of Vibration and Shock
基金
国家自然科学基金(10872063)
关键词
微机械振动式陀螺系统
非线性动力学
时滞反馈控制
分岔
micromachined vibratory gyroscopes system
nonlinear dynamics
feedback control with time delay
bifurcation
