地震作用下高层结构动力响应分析的一种数值方法
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摘要
利用Timoshenko悬臂梁模型,针对高层结构,建立控制体的动力学方程,在时间域上交替运用控制体平动方程和剪力-位移关系式以及控制体转动方程和弯矩-转角关系式,提出一种研究地震作用下高层结构动力响应分析的数值计算方法。数值计算结果表明了该方法的准确性和有效性。数值算例研究了地震作用下高层结构控制体转动惯性的影响、剪切变形和弯曲变形的影响,给出了不同时刻层间剪力的空间分布图。该方法从弯曲波理论角度为研究地震作用下高层结构的动力响应问题提供了一种新的实用工具。
Adopting Timoshenko beam theory, this paper establishes dynamics equations of controlled body. Furthermore, the numerical method analyzing seismic response of high-rise structures is proposed. To describe the vibration of controlled body, the proposed method adopts equations describing body translation-transverse shear relationship and shear-displacement relationship, as well as equations describing body rotation-bending moment relationship and moment-curvature relationship. Two sets of equations are applied alternately in time domain. The accuracy and efficiency of the proposed method are verified by applying it to perform dynamic analysis of a high-rise structure. According to the analysis results, the effects of rotational inertia, shear deformation and bending deformation of controlled body are investigated, and the shear distribution diagram is drawn at different times. The proposed method provides a new practicable tool to analyze dynamic responses of high-rise structures subjected to seismic load.
Adopting Timoshenko beam theory, this paper establishes dynamics equations of controlled body. Furthermore, the numerical method analyzing seismic response of high-rise structures is proposed. To describe the vibration of controlled body, the proposed method adopts equations describing body translation-transverse shear relationship and shear-displacement relationship, as well as equations describing body rotation-bending moment relationship and moment-curvature relationship. Two sets of equations are applied alternately in time domain. The accuracy and efficiency of the proposed method are verified by applying it to perform dynamic analysis of a high-rise structure. According to the analysis results, the effects of rotational inertia, shear deformation and bending deformation of controlled body are investigated, and the shear distribution diagram is drawn at different times. The proposed method provides a new practicable tool to analyze dynamic responses of high-rise structures subjected to seismic load.
引文
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[2]Wu J R,Li Q S.Finite element model updating for a high-rise structure based on ambient vibration measurements[J].Engineering Structures,2004,26:979―990.
[3]Shinji Tanimura,Koji Mimura,Taijiro Nonaka.Dynamic failure of structures due to the great Hanshin-Awaji earthquake[J].International Journal of Impact Engineering,2000,24:583―596.
[4]Yong Lu.An analytical model for dynamic response of beam-column frames to impulsive ground excitations[J].International Journal of Solids and Structures,2007,44:779―798.
[5]杨学林,益德清.多塔楼高层结构振动特性与抗震设计[J].工程力学,2001,18(2):76―81.Yang Xuelin,Yi Deqing.The vibration characteristics and aseismic design of multi-tower-building structures[J].Engingeering Mechanics,2001,18(2):76―81.(in Chinese)
[6]秦荣,梁汉吉,禤强.高层建筑筒体结构动力分析的新方法[J].世界地震工程,2005,21(3):1―6.Qin Rong,Liang Hanji,Xuan Qiang.New method for dynamic analysis of tubular structures in tall buildings[J].World Earthquake Engineering,2005,21(3):1―6.(in Chinese)
[7]邵永松,刘洪波,谢礼立.平面与空间钢框架结构的简化柱梁模型[J].工程力学,2004,21(1):1―8.Shao Yongsong,Liu Hongbo,Xie Lili.The simplified column-beam model for planar and special steel frames[J].Engingeering Mechanics,2004,21(1):1―8.(in Chinese)
[8]Liu Tielin,Liu Kaishin,Zhang Jinxiang.Unstructured gird method for stress wave propagation in elastic media[J].Comput.Methods Appl Mech.Engrg.,2004,193(23-26):2427―2452.
[9]Liu T,Liu K,Zhang J.Triangular grid method for stress-wave propagation in2-D orthotropic materials[J].Archive of Applied Mechanics,2005,74:477―488.
[10]克拉夫R W,彭津J.结构动力学[M].王光远译.北京:科学出版社,1981.Clough R W,Penzien J.Dynamics of Structures[M].Translated by Wang Guangyuan.Beijing:Science Press,1981.(in Chinese)
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