浅埋地下结构底板在竖向地震作用下动力响应

本文研究了地下结构底板在地震竖向分量作用下的动力响应。利用结构动力学和弹性力学的理论,得到底板的运动微分方程,根据边界条件确定底板在的特征频率和振型。针对输入的地震竖向分量的形式,采用分离变量法求解了强迫振动方程.计算时取前三阶振型,采用振型叠加法得到底板的相对位移和绝对位移,并进而求得底板的弯矩,利用求得的弯矩,可以求解底板的受力情况。通过底板的受力情况,可以直观地对地下结构底板进行评价分析,并且推进了地下结构底板抗震理论的研究和发展。

The Dynamic Response of Shallow Buried Underground Structure Bottom Floor under Vertical Seismic Excitation

In this paper the dynamic response of 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 boundary conditions the vibration frequencies and modes of the bottom floor are determined. For the given seismic excitation by using the separation of variables, the differential equation of motion is solved. The relative and absolute displacements of bottom floor are obtained by superposition method with taking the first 3 shape modes. The bending moment of the bottom floor is also obtained. Using the bending moment, the bottom floor’s force condition can be solved. By means of the force condition, it can give the visual evaluation about the underground structure bottom floor to promote the development of underground structure bottom floor’s aseismic theory.