中文摘要：

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．

英文摘要：

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.