Abstract
The cranes simplified as the cantilever beam system. The bending vibration differential equations were built using Hamilton principle.According to discrete differential equations by the finite difference method, the modes of vibration and the natural frequencies can be obtained. Application of discrete time and MATLAB vibration toolbox, the displacement curve and phase on the crane arm can be gotten. And the effect of amplitude angles and lifting loads on the arm vibration had been discussed.The work of the vibration on the crane arm has an universal meaning in the cantilever beams.
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