一种求解地下结构顶板频率和振型的方法
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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.
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.
引文
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[2]国胜兵,赵毅,赵跃堂,等.地下结构在竖向和水平地震荷载作用下的动力分析[J].地下空间,2002,22(4): 314-319. Guo S B,Zhao Y,Zhao Y T,et al.Dynamic analysis of underground structures under the vertical and horizontal seismic load[J].Underground Space,2002,22 (4):314-319.
[3]庄海洋,程绍革,陈国兴.阪神地震中大开站地铁车站震害机制数值仿真分析[J].岩土力学,2008,29(1): 246-250. Zhuang H Y,Cheng S G,Chen G X.Numerical simulation and analysis of earthquake damages of Dakai metro station caused by Kobe earthquake[J].Rock and Soil Mechanics,2008,29(1):246-250.
[4]李国强,李杰.工程结构动力检测理论与应用[M].北京:科学出版社,2002.196-205. Li G Q,Li J.Theory and Application of Dynamic Testing of Structure[M].Beijing:Science Press, 2002.196-205.
[5]蒋济同,王熙堃.一种推导Timoshenko梁频率方程的新方法[J].中国海洋大学学报,2008,36(6):1035- 1039. Jiang J T,Wang X K.A new method for deriving frequency equation of the Timoshenko beam[J].Periodical of Ocean University of China,2008,36(6):1035- 1039.
[6]彭俊生,罗永坤,彭地.结构动力学、抗震计算[M].成都:西南交通大学出版社,2007. Peng J S,Luo Y K,Peng D.Structure Dynamics and Seismic Calculation[M].Chengdu:Southwest Jiaotong University Press,2007.
[7]朱合华,等.地下建筑结构[M].北京:中国建筑工业出版社,2005. ??Zhu H H,et al.Underground Structure[M].Beijing: China Architecture & Building Press,2005.
[8]达维多夫.地下结构的计算与设计[M].北京:高等教育出版社,1957. Da W D F.Calculation and Design of Underground Structure[M].Beijing:Higher Education Press, 1957.
[9]Wood J H.Earthquake design of rectangular underground structures[C]//NZSEE Conference,Wairakei: New Zealand Society for Earthquake Engineering Inc,2005.39-46.
[10]龙驭球.弹性地基梁的计算[M].北京:人民教育出版社,1981. Long Y Q.Calculation of Elastic Foundation Beam [M].Beijing:People's Education Press,1981.
[11]戚承志,陈灿寿,钱七虎,等.浅埋地下结构顶板在竖向地震作用下的动力响应[C]//第2届全国工程安全与防护学术会议论文集.北京:北京建筑工程学院,2010. 865-869. Qi C Z,Chen C S,Qian Q H,et al.Dynamic response of the roof slab of shallowly buried under-ground structure under vertical seismic excitation [C]//Proceedings of the 2nd Na tional Scientific Symposium on engineering safety and protection.Beijing: Beijing University of Civil Engineering and Architecture, 2010.865-869.
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