一种求解地下结构顶板频率和振型的方法  

A Method for Determining Frequencies and Modes of Roof Slab of Underground Structure

作　　者：姚小彬[1] 戚承志[1] 陈国兴[2] 

机构地区：[1]北京建筑工程学院北京市工程结构与新材料工程研究中心,北京100044 [2]南京工业大学岩土工程研究所,南京210009

出　　处：《防灾减灾工程学报》2011年第6期688-694,共7页Journal of Disaster Prevention and Mitigation Engineering

基　　金：北京市教委重点项目;北京市自然基金项目(KZ200810016007);国家自然基金项目(50825403);国家973重大项目(2010CB732003)资助

摘　　要：采用欧拉梁横向自由振动理论,发展了一种求解浅埋地下结构顶板频率和振型的方法。鉴于地下结构顶板频率求解问题的复杂性,首先将该问题假定为平面应变问题求解,推导出浅埋地下结构项板梁的自由振动方程;然后根据顶板梁的边界条件,得到了顶板梁的频率方程,从而得出了顶板梁的频率和振型;进一步得出了墙体转动刚度对顶板频率影响的规律,即转动刚度对顶板低频影响较小,对高频影响较大。还综合考虑土体刚度随埋深的变化和由于土体成拱引起的土体附加质量的变化,研究了结构顶板频率随埋深的变化。这些结果可以为地下结构的动力计算提供参考。A method for determining frequencies and vibration modes of the roof slab of shallowly buried underground structure is developed on the basis of the theory of transverse free vibration of Euler beam on elastic foundation.In view of the complexity of the determination of frequencies for roof slab of underground structure,this problem is assumed to be a plane strain problem.The free vibration equation of the roof slab of shallowly buried underground structure is derived.Then by using the boundary conditions, the frequency equation of the roof slab is obtained.Furthermore,the frequencies and vibration modes of the roof slab is obtained.It is concluded that the rotational stiffness of the side walls has negligible effect on the lower frequencies,but has great impact on the higher frequencies;moreover,the variation in frequencies of roof slab of underground structure with burying depth has been studied by considering the variation in soil stiffness with burying depth and the variation in attached mass of soil with depth burying due to the effect of soil arch.The obtained results may be used as a reference for the underground structure seismic design.

关 键 词：地下结构顶板 自由振动 频率方程 振型 土体拱 

分 类 号：TU311[建筑科学—结构工程]