考虑侧壁影响的偏心单刚体地震响应分析

Seismic analysis of eccentric single-rigid-body considering the influence of colliding-to-wall

地震时建筑内高大器物,如柜体、冰箱等,刚体的晃动、倾倒会导致一定的人员伤亡和经济损失。建筑中多数器物放置在靠近墙体的部位。而已有关于刚体地震响应分析的文献未考虑碰壁的影响。地震过程中,碰壁会改变刚体运动模式,增加刚体的倒塌概率,故考虑碰壁的影响对于模拟刚体的地震响应显得尤为重要。为此,首先利用Lagrange定理建立刚体运动方程;并采用Rosenbrock积分方法建立了刚体摇摆运动响应分析方法;进而提出了“子步-两步法”,以精确地模拟碰地和碰壁两种运动状态变换;最后通过与振动台试验结果对比分析,验证了刚体摇摆运动响应分析方法的可靠性。

During an earthquake,rocking and overturning of high objects in buildings,such as cupboard,refrigerator etc.,may cause certain casualties and economic losses.Most of high objects are located near walls.However,the influence of colliding-to-wall is not considered in existing dynamic analysis of single-rigid-body.Colliding-to-wall changes motion pattern of single-rigid-body,which increases the overturning probability.Therefore,it is particularly important to consider the influence of colliding-to-wall into simulating the dynamic response of single-rigid-body.To solve this problem,the Lagrange’s theorem was adopted to establish equations of motion first.Then a dynamic analysis method of single-rigid-body was proposed based on the Rosenbrock integration method.Subsequently,a multi-step-two-step method was developed to realize state transition before and after colliding to floor and wall.Finally,the reliability of the proposed dynamic analysis method was validated via comparing its results with those of shaking table tests.