厂房下柱在垂直动载下的力学响应及稳定性

针对单层厂房桥式吊车起吊重物时对排架下柱造成冲击的现状,基于振动力学理论,分析垂直动载环境下吊车梁及下柱体组合体系的振动特征,得到下柱垂直位移的动态响应数学表达式,显示振动位移出现两次突增,其中第一次突增伴随位移方向的突跃性改变,成为下柱的最剧烈振动,整个振动持续时间约5.5s。结合具体算例探索相关因素对下柱位移的影响规律,发现增大柱体材质的粘滞系数、弹性模量以及动载衰减系数,可缩短振动时间、降低位移振幅、推迟乃至消除二次位移峰值;而增大起吊重量对振动时间不产生影响,但会使振幅显著增加。在此基础上,以垂直动载对振动系统作功为势函数,采用尖点突变理论建立下柱稳定性状态的判别式,并结合示例阐明通过判别式预测系统稳定时任一参量的方法。

Mechanical Response and Stability of the Lower Columnof Mill Buildings under Vertical Dynamic Load

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.