高墩连续刚构桥纵向振动基频的能量法计算公式
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摘要
为了研究高墩连续刚构桥基频函数表达式,以某一典型桥梁为例,构造了多种不同的桥梁结构形式,建立了64种有限元分析模型,获取了桥梁结构自振特性规律,并提出了桥梁纵向振动的基本振型函数;在此基础上利用瑞利法推导了高墩连续刚构桥纵向振动基频的理论计算公式,最后对此公式的可行性进行了算例验证,讨论了现有抗震规范在此类桥梁结构基频计算上的适用性。结果表明:高墩连续刚构桥第一阶振动以桥墩的纵向振动为主;给出的由能量法得到的基频计算值与有限元模型计算值误差为5%;抗震设计细则中的自振频率计算公式不适用于高墩刚构桥此类非规则桥梁。
In order to obtain the function of fundamental vibration frequency of the rigid frame bridge,firstly,a typical rigid frame bridge with high piers was taken as an example,and 64 similar bridges were fabricated and their finite element(FE) models were set up to obtain the structural natural vibration characteristics,then,the fundamental mode shape function of this type of structure was put forward so as to deduce the theoretical fundamental frequency formula by Rayleigh method.Finally,the presented theoretical formula of fundamental frequency was validated by the engineering and the fundamental frequency formula in the current guidelines for seismic design of highway bridges was discussed therein.The results indicate that the basic oscillation of the rigid frame bridge with high piers consists of the longitudinal vibration of piers,and that the fundamental frequency calculated by the recommended method has an error of 5% compared with the FE result,and the frequency calculation in the guidelines can not be applied to such irregular bridges as the rigid frame bridges.2 tabs,2 figs,15 refs.
In order to obtain the function of fundamental vibration frequency of the rigid frame bridge,firstly,a typical rigid frame bridge with high piers was taken as an example,and 64 similar bridges were fabricated and their finite element(FE) models were set up to obtain the structural natural vibration characteristics,then,the fundamental mode shape function of this type of structure was put forward so as to deduce the theoretical fundamental frequency formula by Rayleigh method.Finally,the presented theoretical formula of fundamental frequency was validated by the engineering and the fundamental frequency formula in the current guidelines for seismic design of highway bridges was discussed therein.The results indicate that the basic oscillation of the rigid frame bridge with high piers consists of the longitudinal vibration of piers,and that the fundamental frequency calculated by the recommended method has an error of 5% compared with the FE result,and the frequency calculation in the guidelines can not be applied to such irregular bridges as the rigid frame bridges.2 tabs,2 figs,15 refs.
引文
[1]黄永玉,赵永刚,赵伟东.基于Lagrange运动方程的悬臂梁的固有频率分析[J].青海大学学报:自然科学版,2011,29(1):12-15.HUANG Yong-yu,ZHAO Yong-gang,ZHAO Wei-dong.Analysis on cantilever beams natural frequencybased on Lagrange motion equation[J].Journal ofQinghai University:Nature Science,2011,29(1):12-15.(in Chinese)
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[6]周建民,吴定俊,李奇,等.墩梁体系自振特性变化规律能量法分析[J].土木工程学报,2006,39(1):60-64.ZHOU Jian-min,WU Ding-jun,LI qi,et al.Variationof free vibration characteristic analysis for pier-beamsystem by energy method[J].China Civil EngineeringJournal,2006,39(1):60-64.(in Chinese)
[7]JTG D60—2004,公路桥涵设计通用规范[S].JTG D60—2004,General specifications for design ofhighway bridges and culverts[S].(in Chinese)
[8]宋一凡.公路桥梁动力学[M].北京:人民交通出版社,2000.SONG Yi-fan.Kinetics of highway bridges[M].Bei-jing:China Communications Press,2000.(in Chinese)
[9]周勇军,贺拴海,宋一凡,等.基于锤击法的弯连续刚构模型桥动力试验[J].振动、测试与诊断,2007,27(3):212-215.ZHOU Yong-jun,HE Shuan-hai,SONG Yi-fan.Dy-namic test of curved continuous rigid frame Bbridgemodel using hammer excitation method[J].Journal ofVibration,Measurement&Diagnosis,2007,27(3):212-215.(in Chinese)
[10]杨昀,周列茅,周勇军.弯桥与高墩[M].北京:人民交通出版社,2011.YANG Yun,ZHOU Lie-mao,ZHOU Yong-jun.Curved bridge with high pier[M].Beijing:ChinaCommunications Press,2011.(in Chinese)
[11]张晓栋.高墩大跨预应力混凝土梁桥振动频率实用计算方法[D].西安:长安大学,2011.ZHANG Xiao-dong.Practical method of fundamentalfrequency for larhge span prestressed concrete girderbridge with high piers[D].Xian:Changan Universi-ty,2011.(in Chinese)
[12]尹海军,李子青,郭琦,等.大跨高墩连续刚构桥动力特性研究[J].西安建筑科技大学学报:自然科学版,2010,42(5):663-668.YIN Hai-jun,LI Zi-qing,GUO qi,et al.Study on thedynamic characteristics of long span continuous rigidframe bridge with high wall piers[J].Journal of XianUniversity of Architecture&Technology:NaturalScience Edition,2010,42(5):663-668.(in Chinese)
[13]曹国俊,何波,袁峰,等.某连续刚构桥动态特性分析[J].华中科技大学学报:城市科学版,2010,27(2):71-73.CAO Guo-jun,HE Bo,YUAn Feng,et al.Dynamiccharacteristics analysis of a continuous rigid framebridge[J].Journal of Huazhong University of Scienceand Technology:Urban Science Edition,2010,27(2):71-73.(in Chinese)
[14]于金良,杨东升.高墩大跨连续刚构桥梁长期健康监测研究[J].筑路机械与施工机械化,2012,29(8):28-30.YU Jin-liang,YANG Dong-shen.Study on healthymonitoring of high-pier and long-span continuous rig-id frame bridge[J].Road Machinery&ConstructionMechanization,2012,29(8):28-30.(in Chinese)
[15]JTG/T B02—01—2008,公路桥梁抗震设计细则[S].JTG/T B02—01—2008,Guidelines for seismic designof highway bridges[S].(in Chinese)
[2]张怀静,潘旦光.变截面连续梁动力特性的半解析解法[J].北京科技大学学报,2008,30(6):590-593,619.ZHANG Huai-jing,PAN Dan-guang.Semi-analyticsolution to dynamic characteristics of non-uniformcontinuous beams[J].Journal of University of Scienceand Technology Beijing,2008,30(6):590-593,619.(in Chinese)
[3]周勇军,贺拴海,宋一凡,等.弹性地基上连续梁桥顺桥向地震振动分析[J].长安大学学报:自然科学版,2008,28(2):49-52.ZHOU Yong-jun,HE Shuan-hai,SONG Yi-fan,et al.Longitudinal seismic vibration of continuous beambridge on elastic foundation[J].Journal of ChanganUniversity:Natural Science Edition,2008,28(2):49-52.(in Chinese)
[4]吴辉琴,王赞芝,涂辉,等.变截面连续梁动力特性的差分解法[J].广西大学学报:自然科学版,2010,35(1):101-104.WU Hui-qin,WANG Zan-zhi,TU Hui,et al.Finite-difference methods for calculating dynamic propertiesof variational continuous beams[J].Journal of Guan-gxi University:Natural Science Edition,2010,35(1):101-104.(in Chinese)
[5]程翔云.关于三跨简支悬索桥振动频率方程的讨论[J].重庆交通学院学报,2001,20(2):22-24.CHENG Xiang-yun.Comments on the vibrational fre-quency equation of three-span simple supported sus-pension bridge[J].Journal of Chongqing Jiaotong In-stitute,2001,20(2):22-24.(in Chinese)
[6]周建民,吴定俊,李奇,等.墩梁体系自振特性变化规律能量法分析[J].土木工程学报,2006,39(1):60-64.ZHOU Jian-min,WU Ding-jun,LI qi,et al.Variationof free vibration characteristic analysis for pier-beamsystem by energy method[J].China Civil EngineeringJournal,2006,39(1):60-64.(in Chinese)
[7]JTG D60—2004,公路桥涵设计通用规范[S].JTG D60—2004,General specifications for design ofhighway bridges and culverts[S].(in Chinese)
[8]宋一凡.公路桥梁动力学[M].北京:人民交通出版社,2000.SONG Yi-fan.Kinetics of highway bridges[M].Bei-jing:China Communications Press,2000.(in Chinese)
[9]周勇军,贺拴海,宋一凡,等.基于锤击法的弯连续刚构模型桥动力试验[J].振动、测试与诊断,2007,27(3):212-215.ZHOU Yong-jun,HE Shuan-hai,SONG Yi-fan.Dy-namic test of curved continuous rigid frame Bbridgemodel using hammer excitation method[J].Journal ofVibration,Measurement&Diagnosis,2007,27(3):212-215.(in Chinese)
[10]杨昀,周列茅,周勇军.弯桥与高墩[M].北京:人民交通出版社,2011.YANG Yun,ZHOU Lie-mao,ZHOU Yong-jun.Curved bridge with high pier[M].Beijing:ChinaCommunications Press,2011.(in Chinese)
[11]张晓栋.高墩大跨预应力混凝土梁桥振动频率实用计算方法[D].西安:长安大学,2011.ZHANG Xiao-dong.Practical method of fundamentalfrequency for larhge span prestressed concrete girderbridge with high piers[D].Xian:Changan Universi-ty,2011.(in Chinese)
[12]尹海军,李子青,郭琦,等.大跨高墩连续刚构桥动力特性研究[J].西安建筑科技大学学报:自然科学版,2010,42(5):663-668.YIN Hai-jun,LI Zi-qing,GUO qi,et al.Study on thedynamic characteristics of long span continuous rigidframe bridge with high wall piers[J].Journal of XianUniversity of Architecture&Technology:NaturalScience Edition,2010,42(5):663-668.(in Chinese)
[13]曹国俊,何波,袁峰,等.某连续刚构桥动态特性分析[J].华中科技大学学报:城市科学版,2010,27(2):71-73.CAO Guo-jun,HE Bo,YUAn Feng,et al.Dynamiccharacteristics analysis of a continuous rigid framebridge[J].Journal of Huazhong University of Scienceand Technology:Urban Science Edition,2010,27(2):71-73.(in Chinese)
[14]于金良,杨东升.高墩大跨连续刚构桥梁长期健康监测研究[J].筑路机械与施工机械化,2012,29(8):28-30.YU Jin-liang,YANG Dong-shen.Study on healthymonitoring of high-pier and long-span continuous rig-id frame bridge[J].Road Machinery&ConstructionMechanization,2012,29(8):28-30.(in Chinese)
[15]JTG/T B02—01—2008,公路桥梁抗震设计细则[S].JTG/T B02—01—2008,Guidelines for seismic designof highway bridges[S].(in Chinese)
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