考虑主塔刚度影响的三塔自锚式悬索桥竖弯频率计算公式
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摘要
为方便计算多塔自锚式悬索桥的竖向自振频率,基于最简单的多塔自锚式悬索桥形式——三塔自锚式悬索桥,考虑主塔刚度对振动频率的影响,应用Rayleigh法,推导了1阶反对称和正对称竖弯振动频率计算公式,并提出主塔刚度影响系数的表达式。公式的精确性采用缩尺模型的模态测试结果和实际桥梁的数值分析结果进行验证。研究结果表明:主塔刚度对于三塔自锚式悬索桥的竖弯刚度影响较大,进行频率计算时不可忽略;影响程度可以通过给出的主塔刚度影响系数计算公式进行计算;公式计算结果与模态识别结果和数值分析结果的误差率均在3%以内,表明给出的公式具有较高的计算精度。
In order to calculate vertical vibration frequencies of multi-tower self-anchored suspension bridge(MSSB)conveniently,the three-tower self-anchored suspension bridge(TSSB)was taken as research object,which is the simplest type of MSSB.Based on the Rayleigh method,frequency formulas for 1st anti-symmetric and symmetric vertical vibration modes of TSSB were derived in consideration of the influence of tower stiffness on vibration frequencies.The modal test results of scaled TSSB and numerical analysis result of TSSB were taken as examples to check the accuracy of proposed formulas respectively.The results show that:vertical frequencies are significantly affected by tower stiffness of TSSB and the extent of influence can be assessed by the main tower stiffness coefficients formulas.The errors between formulas calculation result and modal test result or numerical analysis result are within 3%,which shows the good accuracy of the frequency formulas.
In order to calculate vertical vibration frequencies of multi-tower self-anchored suspension bridge(MSSB)conveniently,the three-tower self-anchored suspension bridge(TSSB)was taken as research object,which is the simplest type of MSSB.Based on the Rayleigh method,frequency formulas for 1st anti-symmetric and symmetric vertical vibration modes of TSSB were derived in consideration of the influence of tower stiffness on vibration frequencies.The modal test results of scaled TSSB and numerical analysis result of TSSB were taken as examples to check the accuracy of proposed formulas respectively.The results show that:vertical frequencies are significantly affected by tower stiffness of TSSB and the extent of influence can be assessed by the main tower stiffness coefficients formulas.The errors between formulas calculation result and modal test result or numerical analysis result are within 3%,which shows the good accuracy of the frequency formulas.
引文
[1]Ren W X,Blandford G E,Harik I E.Roebling suspension bridge.I:Finite-element model and free vibration response[J].Journal of Bridge Engineering,2004,9(2):110-118.
[2]韩大建,苏成,王乐文,等.香港汀九大桥动力特性研究[J].华南理工大学学报:自然科学版,1999,27(11):29-35.HAN Da-jian,SU Cheng,WANG Le-wen,et al.A study on the dynamic behavior of the Hong Kong Ting Kau Bridge[J].Journal of South China University of Technology:Natural Science Edition,1999,27(11):29-35.(in Chinese)
[3]刘春华,秦权.悬索桥振动特性对结构参数的灵敏度[J].清华大学学报:自然科学版,1998,38(12):48-51.LIU Chun-hua,QIN Quan.Sensitivities of natural modes of suspension bridges to structural parameters[J].Jounal of Tsinghua University:Science and Technology,1998,38(12):48-51.(in Chinese)
[4]张运波,陈伟,林玉森.影响大跨度悬索桥自振特性的参数分析[J].华东公路,2002(6):3-6.ZHANG Yun-bo,CHEN Wei,LIN Yu-sen.Parameter analysis on natural frequency of long span suspension bridge[J].East China Highway,2002(6):3-6.(in Chinese)
[5]刘春华,秦权.桥梁结构固有频率的统计特征[J].中国公路学报,1997,10(4):49-54.LIU Chun-hua,QIN Quan.Statistics of natural frequencies for bridge structures[J].China Journal of Highway and Transport,1997,10(4):49-54.(in Chinese)
[6]Liu X G,Fan J S,Nie J G,et al.Behavior of composite rigid frame bridge under bi-directional seismic excitations[J].Journal of Traffic and Transportation Engineering:English Edition,2014,1(1):62-71.
[7]肖汝诚.吊桥结构自振频率的计算方法[J].华东公路,1991(1):54-58.XIAO Ru-cheng.Method to calculate natural vibration frequency of suspension bridges[J].East Road,1991(1):54-58.(in Chinese)
[8]鞠小华,廖海黎,沈锐利.对悬索桥对称竖弯基频近似公式的修正[J].土木工程学报,2002,35(1):44-49.JU Xiao-hua,LIAO Hai-li,SHEN Rui-li.Modification on simplified formula of symmetric vertical natural frequencies for suspension bridges[J].China Civil Engineering Journal,2002,35(1):44-49.(in Chinese)
[9]Yoshida O,Okuda M,Moriya T.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):454-463.
[10]周敉,王君杰,袁万城.自锚式悬索桥地震反应有限元分析[J].长安大学学报:自然科学版,2008,28(1):66-71.ZHOU Mi,WANG Jun-jie,YUAN Wan-cheng.Seismic response analysis and simulation of self-anchored suspension bridge based on ANSYS[J].Journal of Chang’an University:Natural Science Edition,2008,28(1):66-71.(in Chinese)
[11]梁鹏,吴向男,李万恒,等.三塔悬索桥汽车效应几何非线性[J].长安大学学报:自然科学版,2011,31(4):45-49.LIANG Peng,WU Xiang-nan,LI Wan-heng,et al.Geometrical nonlinearity under live load for three-tower suspension bridges[J].Journal of Chang’an University:Natural Science Edition,2011,31(4):45-49.(in Chinese)
[12]刘斌.三塔悬索桥振动特性的研究[D].成都:西南交通大学,2009.LIU Bin.Vibration characteristics research on threetower suspension bridge[D].Chengdu:Southwest Jiao tong University,2009.(in Chinese)
[13]张超.多塔自锚式悬索桥竖弯基频简化计算[J].武汉理工大学学报:交通科学与工程版,2013,37(4):753-757.ZHANG Chao.Simplified calculation of primary vertical frequencies for multi-tower self-anchored suspension bridge[J].Journal of Wuhan University of Technology:Transportation Science and Engineering,2013,37(4):753-757.(in Chinese)
[14]邓育林,彭天波,李建中.大跨多塔悬索桥纵向地震碰撞反应参数研究[J].振动与冲击,2011,30(4):205-210.DENG Yu-lin,PENG Tian-bo,LI Jian-zhong.Parametric study on longitudinal seismic pounding response for a long-span multi-tower suspension bridge[J].Journal of Vibration and Shock,2011,30(4):205-210.(in Chinese)
[15]张超.三塔自锚式悬索桥动力特性及地震响应研究[D].福州:福州大学,2011.ZHANG Chao.Study on dynamic characteristics and seismic response of self-anchored suspension bridge with three-tower[D].Fuzhou:Fuzhou University,2011.(in Chinese)
[16]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1992.LI Guo-hao.Stability and vibration of bridge structure[M].Beijing:China Railway Publishing House,1992.(in Chinese)
[2]韩大建,苏成,王乐文,等.香港汀九大桥动力特性研究[J].华南理工大学学报:自然科学版,1999,27(11):29-35.HAN Da-jian,SU Cheng,WANG Le-wen,et al.A study on the dynamic behavior of the Hong Kong Ting Kau Bridge[J].Journal of South China University of Technology:Natural Science Edition,1999,27(11):29-35.(in Chinese)
[3]刘春华,秦权.悬索桥振动特性对结构参数的灵敏度[J].清华大学学报:自然科学版,1998,38(12):48-51.LIU Chun-hua,QIN Quan.Sensitivities of natural modes of suspension bridges to structural parameters[J].Jounal of Tsinghua University:Science and Technology,1998,38(12):48-51.(in Chinese)
[4]张运波,陈伟,林玉森.影响大跨度悬索桥自振特性的参数分析[J].华东公路,2002(6):3-6.ZHANG Yun-bo,CHEN Wei,LIN Yu-sen.Parameter analysis on natural frequency of long span suspension bridge[J].East China Highway,2002(6):3-6.(in Chinese)
[5]刘春华,秦权.桥梁结构固有频率的统计特征[J].中国公路学报,1997,10(4):49-54.LIU Chun-hua,QIN Quan.Statistics of natural frequencies for bridge structures[J].China Journal of Highway and Transport,1997,10(4):49-54.(in Chinese)
[6]Liu X G,Fan J S,Nie J G,et al.Behavior of composite rigid frame bridge under bi-directional seismic excitations[J].Journal of Traffic and Transportation Engineering:English Edition,2014,1(1):62-71.
[7]肖汝诚.吊桥结构自振频率的计算方法[J].华东公路,1991(1):54-58.XIAO Ru-cheng.Method to calculate natural vibration frequency of suspension bridges[J].East Road,1991(1):54-58.(in Chinese)
[8]鞠小华,廖海黎,沈锐利.对悬索桥对称竖弯基频近似公式的修正[J].土木工程学报,2002,35(1):44-49.JU Xiao-hua,LIAO Hai-li,SHEN Rui-li.Modification on simplified formula of symmetric vertical natural frequencies for suspension bridges[J].China Civil Engineering Journal,2002,35(1):44-49.(in Chinese)
[9]Yoshida O,Okuda M,Moriya T.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):454-463.
[10]周敉,王君杰,袁万城.自锚式悬索桥地震反应有限元分析[J].长安大学学报:自然科学版,2008,28(1):66-71.ZHOU Mi,WANG Jun-jie,YUAN Wan-cheng.Seismic response analysis and simulation of self-anchored suspension bridge based on ANSYS[J].Journal of Chang’an University:Natural Science Edition,2008,28(1):66-71.(in Chinese)
[11]梁鹏,吴向男,李万恒,等.三塔悬索桥汽车效应几何非线性[J].长安大学学报:自然科学版,2011,31(4):45-49.LIANG Peng,WU Xiang-nan,LI Wan-heng,et al.Geometrical nonlinearity under live load for three-tower suspension bridges[J].Journal of Chang’an University:Natural Science Edition,2011,31(4):45-49.(in Chinese)
[12]刘斌.三塔悬索桥振动特性的研究[D].成都:西南交通大学,2009.LIU Bin.Vibration characteristics research on threetower suspension bridge[D].Chengdu:Southwest Jiao tong University,2009.(in Chinese)
[13]张超.多塔自锚式悬索桥竖弯基频简化计算[J].武汉理工大学学报:交通科学与工程版,2013,37(4):753-757.ZHANG Chao.Simplified calculation of primary vertical frequencies for multi-tower self-anchored suspension bridge[J].Journal of Wuhan University of Technology:Transportation Science and Engineering,2013,37(4):753-757.(in Chinese)
[14]邓育林,彭天波,李建中.大跨多塔悬索桥纵向地震碰撞反应参数研究[J].振动与冲击,2011,30(4):205-210.DENG Yu-lin,PENG Tian-bo,LI Jian-zhong.Parametric study on longitudinal seismic pounding response for a long-span multi-tower suspension bridge[J].Journal of Vibration and Shock,2011,30(4):205-210.(in Chinese)
[15]张超.三塔自锚式悬索桥动力特性及地震响应研究[D].福州:福州大学,2011.ZHANG Chao.Study on dynamic characteristics and seismic response of self-anchored suspension bridge with three-tower[D].Fuzhou:Fuzhou University,2011.(in Chinese)
[16]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1992.LI Guo-hao.Stability and vibration of bridge structure[M].Beijing:China Railway Publishing House,1992.(in Chinese)
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