Abstract
According to the energy method, the dynamic stability of a crane's telescopic boom under the periodic load is studied, which is known as parametric resonance, based on the design code for a crane (GB/T3811-2008), the stability analysis model of the box telescopic boom can be regarded as variable-section stepped columns. The parametric vibration equation of n-stepped columns which expressed as Mathieu Equation is deduced by the Hamilton Principle, then the Critical frequency equation of dynamic instability regions of the telescopic booms are derived, finally, the effects of damping to the dynamic stability of telescopic boom are discussed. The results show that, the dynamic instability regions are reduced when the damping coefficient is increased and the effect on the second dynamic instability region is more obvious, that means damping improves the structure's dynamic stability.
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