Abstract:When bridge cranes lift heavy weights, the load is borne by the lower column of single-storey mill buildings. In view of this fact, the mathematical expression of dynamic response of the lower column's vertical displacement was deduced by analyzing the vibration characteristics of the system composed of the crane beam and lower column under vertical dynamic load. The mathematical expression based on the theory of vibration mechanics showed that the vibration lasts about 5.5 s and that the vertical vibration displacement has two sudden increases. The first sudden increase of displacement is the most severe vibration of the lower column. By specific example, several factors influencing the vibration were researched. The results showed that if we increased the viscosity coefficient and elastic modulus of column material and the attenuation coefficient of dynamic load, then the vibration time is shortened, the displacement amplitude is reduced, and the peak of the second displacement is postponed or eliminated altogether. Increasing the lifting weight had no effect on the vibration duration, but did increase the amplitude significantly. On this basis, taking the work of vertical dynamic load as the potential function, the cusp catastrophe theory was used to establish the discriminant formula of the stability state of the lower column, and the method of predicting any parameter in the stable system is illustrated.
