行波输入下双单自由度体系结构的最大振动相对位移
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摘要
在地震行波输入下,双单自由度体系结构由于行波激励引起的不同向振动会导致较大的相对位移。基于随机振动理论方法,首先推导行波输入下双单自由度体系结构最大振动的相对位移公式,然后分析该结构的结构动力特性对相关系数的影响。研究结果表明:结构的相关系数及其幅值会随着两相邻结构基本周期数值的接近而增大,相关系数会随着结构阻尼比的增大而增大。然后在相关系数的幅值特性进行研究和参数分析结果的基础上提出了最小周期比限值拟合曲线,结果表明当双单自由度体系结构的最小周期比小于最小周期比限值时,系统的最大振动相对位移计算公式中可以忽略相关系数的影响,从而使计算大为简化。最后通过工程实例描述最大振动相对位移计算公式的工程应用。研究结果对该类体系结构在实际工程中的应用具有一定的理论和指导意义。
In the traveling seismic wave input,a greater relative displacement of two single-degree-of-freedom systems were caused due to different vibrations.Based on the theory of random vibration method,the maximum vibration displacement formula was deduced and the correlation coefficient was studied.Analysis results show that when the two adjacent structure natural periods are more close,the correlation coefficient and its amplitude are bigger,and when the difference of natural periods is great,correlation coefficient is small;The damping ratio is higher when the correlation coefficients is larger.Based on the correlation coefficient amplitude characteristic research and the results of parameter analysis,the curve fitting of minimal period ratio Limit value was put forward.When the minimal period ratio of the two single degree of freedom systems is less than its limit value,the maximum vibration displacement calculation formula may can ignore the effect of correlation coefficient.Finally,through an example the engineering application of the maximum vibration displacement formula was demonstrated.The results of this study have certain theoretical significance and guidance on the application in actual project.
In the traveling seismic wave input,a greater relative displacement of two single-degree-of-freedom systems were caused due to different vibrations.Based on the theory of random vibration method,the maximum vibration displacement formula was deduced and the correlation coefficient was studied.Analysis results show that when the two adjacent structure natural periods are more close,the correlation coefficient and its amplitude are bigger,and when the difference of natural periods is great,correlation coefficient is small;The damping ratio is higher when the correlation coefficients is larger.Based on the correlation coefficient amplitude characteristic research and the results of parameter analysis,the curve fitting of minimal period ratio Limit value was put forward.When the minimal period ratio of the two single degree of freedom systems is less than its limit value,the maximum vibration displacement calculation formula may can ignore the effect of correlation coefficient.Finally,through an example the engineering application of the maximum vibration displacement formula was demonstrated.The results of this study have certain theoretical significance and guidance on the application in actual project.
引文
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[2]伍松,张新培,高少波,等.超长混凝土框架结构地震反应行波效应研究[J].世界地震工程,2011,27(2):219-224.WU Song,ZHANG Xinpei,GAO Shaobo,et al.Research on seismic response of over-long RC frame considering traveling wave effect[J].World Earthquake Engineering,2011,27(2):219-224.
[3]焦常科,李爱群,操礼林,等.三塔悬索桥行波效应研究[J].土木工程学报,2010,43(12):100-106.JIAO Changke,LI Aiqun,CAO Lilin,et al.Traveling wave influence analysis for triple-tower suspension bridges[J].China Civil Engineering Journal,2010,43(12):100-106.
[4]Bi K,Hao H,Chouw B.Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding[J].Earthquake Engineering and Structural Dynamics,2010,39(3):303-323.
[5]HAO Hong.A parametric study of the required seating length for bridge decks during earthquake[J].Earthquake Engineering and Structural Dynamics,1998,27(1):91-103.
[6]何庆祥,沈祖炎.结构地震行波效应分析综述[J].地震工程与工程振动,2009,29(1):50-57.HE Qingxiang,SHEN Zuyan.Review of structural seismic analysis of travelling wave effects[J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(1):50-57.
[7]周光伟,李建中,范立础.连续梁桥行波输入下支承长度的参数分析[J].湖南大学学报:自然科学版,2008,35(10):6-10.ZHOU Guangwei,LI Jianzhong,FAN Lichu.Parametric study of the required seating length for continuous bridges under longitudinal excitation of traveling seismic wave[J].Journal of Hunan University:Natural Sciences,2008,35(10):6-10.
[8]张静娟,高大峰,刘伯栋.多跨连续梁桥地震行波效应分析[J].水利与建筑工程学报,2009,7(2):114-116.ZHANG Jingjuan,GAO Dafeng,LIU Bodong.Seismic response analysis for continuous beam bridge under excitation of traveling waves[J].Journal of Water Resources and Architectural Engineering,2009,7(2):114-116.
[9]Zanardo G,Hao H,Modena C.Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion[J].Earthquake Engineering and Structural Dynamics,2002,31(6):1325-1345.
[10]Jankowski R,Wilde K,Fujino Y.Pounding of superstructure segments in isolated elevated bridge during earthquakes[J].Earthquake Engineering and Structural Dynamics,1998,27(5):487-502.
[11]高玉峰,蒲黔辉,李晓斌.梁式桥地震碰撞响应及防碰撞与落梁措施研究进展[J].地震工程与工程振动,2011,31(1):80-88.GAO Yufeng,PU Qianhui,LI Xiaobin.State-of-arts of earthquake-induced pounding responses of girder bridges and measures for preventing pounding and span collapse[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(1):80-88.
[12]Nigam N C.随机振动概论[M].何成慧,周鉴如,陈文良,等译.上海:上海交通大学出版社,1985:192-194.Nigam N C.Introduction to random vibrations[M].HE Chenghui,ZHOU Jianru,CHEN Wenliang,et al.trans.Shanghai:Shanghai Jiao Tong University Press,1985:192-194.
[13]胡聿贤.地震工程学[M].2版.北京:地震出版社,2006:40-66.HU Yuxian.Earthquake engineering[M].2nd ed.Beijing:Seismological Press,2006:40-66.
[14]JTG/TB02-01-2008,公路桥梁抗震设计细则[S].JTG/TB02-01-2008,Guidelines for seismic design of highway bridges[S].
[15]何度心,黄龙生,陆干文,等.桥梁抗震计算[M].北京:地震出版社,1991:24-28.HE Duxin,HUANG Longsheng,LU Ganwen,et al.Seismic design of bridges[M].Beijing:Seismological Press,1991:24-28.
[16]周光伟,李建中,范立础.多跨连续梁桥纵桥向动力特性研究及其地震反应谱简化分析[J].交通与计算机,2008,26(5):1-5.ZHOU Guangwei,LI Jianzhong,FAN Lichu.Research on dynamic characteristic of multispan continuous bridges in span direction and its seismic analysis of response spectrum[J].Computer and Communications,2008,26(5):1-5.
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