Abstract：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.
2015, Vol. 36 
