摘要
模态耦合是摩擦引起系统自激振荡的主要不稳定性机理之一。针对此类问题,构建了两自由度非线性质量-传动带系统。首先,通过劳斯判据分析系统的稳定性,给出了计算Hopf分岔点的数学表达式以及系统参数改变时分岔点和特征值分岔图的变化状态。其次,将扩展谐波平衡法加以利用和延伸,得到了自激振荡系统极限环幅值的解析解,进而研究了系统外界参数和结构参数变化对极限环幅值的影响。外界参数(带速和摩擦系数)变化可造成极限环幅值的规律性变化,而结构参数(阻尼比和固有频率)的改变会引起极限环幅值复杂的动力学行为。研究方法及结果可为机械系统结构设计和减振等方面提供理论分析参考。
Mode-coupling is one of the major unstable mechanisms in friction induced self-excited oscillation systems. This paper constructs a 2-DOF nonlinear mass-conveyor belt system in order to analyze this problem. Using the Routh criterion, the mathematical expression of the Hopf bifurcation point is given out. At the same time, the variation state of the bifurcation point and the eigenvalue bifurcation diagrams are also presented when the system parameters change. The extended harmonic balance method is advanced, through which the analytic solutions of the limit cycle amplitude of the self-excited oscillation system are obtained. Further more, the effects of the outside and the structural parameter changes on the limit cycles are investigated. Discussions demonstrate that the change of the outside parameters (belt velocity and friction coefficient) will lead to regular variations of limit cycle amplitudes, while the change of the structural parameters (damping ratio and natural frequency) will induce complex dynamic behaviors of the limit cycles. The research method and results may provide a theoretical analysis reference for the structure design of mechanical systems as well as vibration reduction.
出处
《振动工程学报》
EI
CSCD
北大核心
2009年第4期363-370,共8页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(50575180)
西安理工大学优秀博士学位论文研究基金资助项目
关键词
自激振荡
摩擦
极限环
模态耦合
self-excited oscillation
friction
limit cycle
mode-coupling