自由端受磁力吸引悬臂梁的非线性振动  

NONLINEAR VIBRATIONS OF A CANTILEVER SUBJECT TO A MAGNETIC FORCE OF ATTRACTION AT THE FREE END

作　　者：张国策[1] 陈立群[1,2] 丁虎[1,2] 

机构地区：[1]上海大学理学院,上海200444 [2]上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《固体力学学报》2015年第4期277-282,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金重点项目(11232009);上海市重点学科建设项目(S30106)资助

摘　　要：研究了含分式函数的非线性磁力系统的受迫振动.磁铁吸引力横向作用在悬臂梁自由端处.根据含有非线性边界的连续体模型,给出了非平凡静平衡位形.以稳定位形作坐标变换后,计算了相应的固有频率,并求得微幅受迫振动稳态响应的近似解析解.研究了不同磁铁间距与频响曲线的关系,结果表明磁力方向和大小对它们均有较大影响.数值结果与解析结果吻合得很好.The forced vibration of a cantilevered magnetic system is investigated. One small magnet, fixed at the free end,is perpendicularly attracted by the other magnet. The magnetic force is modeled as a fractional function. The nontrivial static equilibrium configuration is derived from the distributed parameter model with the nonlinear boundary. A coordinate transform is introduced only based on the stable nontrivi al equilibrium. The effects of system parameters on the natural frequency are shown. The steady-state re- sponse of the forced vibration is approximately determined under a small harmonic base excitation. The effect of the initial distance between the two magnets on the frequency-response curve is also presented. The finite difference method is employed to numerically validate these analyzed results, It is concluded that a change in magnitude or direction of the magnetic force has a great effect on the equilibrium, the natural frequency or the steady-state response.

关 键 词：非线性 连续体 静平衡位形 固有频率 受迫振动 

分 类 号：O322[理学—一般力学与力学基础]