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| Nonlinear vibrations of a cantilever subject to a magnetic force of attraction at the free end |
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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.
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Received: 19 August 2014
Published: 28 August 2015
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2015, Vol. 36 
