高层建筑筒体结构的共振响应
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摘要
为了计算高层建筑筒体结构的共振响应,将其简化成能同时考虑弯曲、剪切、轴向变形和扭转变形的广义Timoshenko悬臂梁。利用Hamilton原理,导出高层筒体结构在相应于各种变形的地震激励下的位移响应控制微分方程及相应的边界条件后,利用常微分方程求解器进行求解。通过对计算结果的分析,讨论了影响共振响应的因素,并得出了相当合理的结论:即当激励荷载的频率与结构体系的自振频率很接近时,结构的反应会出现非常大的突变。
In order to calculate the resonant response of tubular structure of high-rise buildings,a generalized Timoshenko cantilever beam considering bending,shear,axial and torsional deformation was adopted.Based on the Hamiltonian principle,the differential equations of the displacement response under seismic excitations associated with the deformation of tubular structure of high-rise buildings and corresponding boundary conditions were derived.These equations were solved using ordinary differential equation solver.After analyzing the results,the factors that affect the resonant response were discussed,and a reasonable conclusion was obtained.It is found that the response of the structure increase enormously when the frequency of the excitation load is very close to the natural frequency of the structure.
In order to calculate the resonant response of tubular structure of high-rise buildings,a generalized Timoshenko cantilever beam considering bending,shear,axial and torsional deformation was adopted.Based on the Hamiltonian principle,the differential equations of the displacement response under seismic excitations associated with the deformation of tubular structure of high-rise buildings and corresponding boundary conditions were derived.These equations were solved using ordinary differential equation solver.After analyzing the results,the factors that affect the resonant response were discussed,and a reasonable conclusion was obtained.It is found that the response of the structure increase enormously when the frequency of the excitation load is very close to the natural frequency of the structure.
引文
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[2]LI QS,FANG J O,JEARY AP.Free vibration analysis of cantilevered tall structures under various axial loads[J].Jour-nal of Engineering Structures,2000,22:525-534.
[3]LI Q S,CAO H,LI G.Analysis of free vibrations of tall buildings[J].ASCE,Journal of Engineering Mechanics,1994,120(9):1 861-1 876.
[4]王光远,建筑结构的振动[M].北京:科学技术出版社,1978:168-178.
[5]李桂青,抗震结构计算理论和方法[M].北京:地震出版社,1985:342-354.
[6]Wen-Hae Lee.Free vibration analysis for tube-in-tube tall buildings[J].Journal of Sound and Vibration,2007,303:287-304.
[7]龚耀清,包世华.超高层建筑空间巨型框架自由振动计算的新方法[J].工程力学,2008,25(10):133-140.
[8]龚耀清,兰自贤.超高层建筑空间巨形框架-核心筒结构的共振响应[J].工程力学,2009,26(3):55-63.
[9]袁驷.介绍一个常微分方程边值问题通用程序——COLSYS[J].计算结构力学及其应用,1990,7(2):104-105.
[10]包世华,张铜生.高层建筑结构设计和计算[M].北京:清华大学出版社,2007.
[11]龚耀清,包世华,龙驭球.弹性地基上高层建筑结构对确定性动力作用的稳态反应[J].工程力学,2000,17(2):1-9.
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