自由端受磁力吸引悬臂梁的非线性振动

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。

Nonlinear vibrations of a cantilever subject to a magnetic force of attraction at the free end

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 nontrivial equilibrium. The effects of system parameters on the natural frequency are shown. The steady-state response 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.