一类非线性磁流变系统局部分岔特性研究

ONE LOCAL BIFURCATION OF NONLINEAR SYSTEM BASED ON MAGNETORHEOLOGICAL DAMPER^1

讨论了一类基于磁流变阻尼器非线性系统的局部分岔与控制问题,建立了该系统的动力学模型,运用中心流形定理和范式理论,得到该系统双零特征值问题的规范形及其普适开折,进而探讨了此系统的分岔行为和稳定性;给出了分岔曲线、转迁集;并给出了此类非线性系统的数值仿真结果.

Magnetorheological (MR) fluids is a kind of smart materials, it can be transformed from Newton fluids into visco-plastic solid by varying the strength of the magnetic field. The dampers made by MR fluids have a number of attractive features, for example, inexpensive to manufacture, small power requirements, reliability, stability, and can continually change its state. The process of change is very quick, less than a few milliseconeds, and can be easily controlled. MR dampers have been recognized as having many attractive characteristics for use in vibration control applications, it is a kind of ideal semi-active control devices. MR damper is widely used in the civil engineering, vehicle suspension system and its structural characteristics have been extensively studied. But, up to now, the dynamic behaviors about MR damper semi-active control system, specially, its bifurcation behaviors and global dynamics have not been discussed. The problem of bifurcation behavior for the MR damper nonlinear system is discussed. A dynamic model of the system with nonlinear MR damper force is presented. The system's normal form and universal unfolding of the double zero eigenvalue are achieved. The complex dynamic behavior of the nonlinear system will be shown by the analysis. By theoretical analysis, it is shown that the design of parameters has a close relation with the system's stability; the range of selected parameters are achieved when the system is stable, based on the condition of bifurcation parameters, bifurcation curve, bifurcation set and phase portraits. From numerical simulating analysis, the complex dynamics behavior is shown, and the result is in correspondence with the theoretic analysis.