四边固支下地下结构底板竖向地震作用下动力响应

Dynamic Response of Completed Clamped Supported Underground Structure Bottom Floor Under Vertical Seismic Excitation

研究四边固定支撑情况下的地下结构底板在竖向地震作用下的动力近似解析解,首先得到结构底板的运动微分方程,通过采用结构动力学与弹性力学理论基础,并且依照四边固定支撑情况计算底板特征频率和振型.在输入地震竖向分量的振动形式后运用分离变量法解出受迫振动方程的特解,计算得到底板的相对位移和绝对位移,通过位移继续求解底板的受力情况.根据底板受力情况,对地下结构进行抗震性能分析.

In this paper the dynamic approximate analytic solution of completed clamped supported underground structure under vertical seismic excitation is studied. The differential equation of motion of bottom slab is obtained by using the related theories of structural mechanics and elasticity. Using the conditions which are completed clamped supported the vibration frequencies and modes of the bottom floor are determined. For the given seismic excitation by using the separation of variables differential equation of motion the forced vibration equation is solved. The relative and absolute displacements of bottom floor are obtained by superposition method. Using the relative and absolute displacements of bottom floor, the bottom floor＇ s force condition can be solved. By means of the force condition, it can be doing seismic performance analysis of underground structures.