曲线桥抗震精细传递矩阵法
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摘要
根据曲线梁桥在竖直方向的弯扭耦合和水平方向的弯曲、轴向变形,导出了曲线梁单元竖直方向和水平方向的精细传递矩阵;给出了用精细传递矩阵法计算曲线梁桥竖直方向和水平方向的振动频率、振型、地震内力和变形的计算公式和步骤,并运用精细传递矩阵法对单跨简支桥进行了地震反应分析.算例表明,本方法简单、具有较高精度和效率.
Considering the curved bridge' coupling of the bending and torsion in the vertical direction,as well as the bending and axial deformation in the horizontal direction,the precise transfer matrixs of the beam elements are derived in the vertical and horizontal directions.The formulation and steps are present for calculating the horizontal and vertical vibration frequencies,vibration modes,seismic force and the deformation by the precise transfer matrix method.It has been applied to do the research the earthquake response of single-span curved bridge.The example shows that this method is simple,effective and of high precision.
Considering the curved bridge' coupling of the bending and torsion in the vertical direction,as well as the bending and axial deformation in the horizontal direction,the precise transfer matrixs of the beam elements are derived in the vertical and horizontal directions.The formulation and steps are present for calculating the horizontal and vertical vibration frequencies,vibration modes,seismic force and the deformation by the precise transfer matrix method.It has been applied to do the research the earthquake response of single-span curved bridge.The example shows that this method is simple,effective and of high precision.
引文
[1]李青宁,李进,焦驰宇,等.大跨度拱桥振动传递分析[C]∥第八届全国振动理论及应用学术会议论文集.上海:同济大学出版社,2003.LI Qing-ning,LI Jin,JIAO Chi-yu,et al.Vibration transfer analysis oflong-span arch bridge[C]∥Proceedings of the8th conference on vibration theory and application.Shanghai:TongJi University Press,2003.
[2]尹海军,徐雷,申跃奎,等.汶川地震中桥梁损伤机理探讨[J].西安建筑科技大学学报:自然科学版,2008,16(5):672-677.YIN Hai-jun,XU Lei,SHEN Yue-kui,et al.Study on the seismic damages to the bridges in Wenchuan Earthquake[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition),2008,16(5):672-677.
[3]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(4):131-136.ZHONG Wan-xie.Precise time-intergration method for structural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131-136.
[4]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,33(1):18-23.LI Qing-ning.The transfer matrix method of bar elements with variable cross-section[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition),2001,5(1):18-23.
[5]李青宁.抛物线连拱精确计算的传递矩阵法[J].西安建筑科技大学学报(自然科学版),1998,20(3):67-70.LI Qing-ning.Transfer matrix method for the accurate calculation of parabolic multi arch[J].J.of Xi′an Univ.of Arch.&Tech.(Natural Science Edition),1998,18(3):67-70.
[6]瞿尔仁,刘孝武,易云焜,等.传递矩阵法在曲线桥结构中的应用[J].合肥工业大学学报:自然科学版,1999,16(6):77-83.QU Er-ren,LI U Xiao-wu,YI Yun-kun,et al.Transfer matrix method applied to structural analysis of curve bridge[J].Journal of Hefei University of Technology(Natural Science Edition),1999,16(6):77-83.
[7]魏双科.曲线梁桥的固有振动特性及地震反应分析[D].南京:南京工业大学,2006.WEI Shuang-ke.Natural dynamic characteristics and seismic response analysis of curved girder bridges[D].Nanjing:Nanjing University of Technology,2006.
[8]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191～195.
[9]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.LI U Qing-tan,NI Guo-rong.The transfer matrix method used in structure analysis[M].Beijing:China Rail way Press,1997.
[10]米彩盈,安琪,李芾.基于传递矩阵法的轮对固有频率计算方法[J].交通运输工程学报,2006,6(4):20-26.MI Cai-ying,AN Qi,LI Fu.Calculation method of wheelset natural frequency based on transfer matrixes[J].Journal of Traffic and Transportation Engineering,2006,6(4):20-26.
[11]GB50191-93,构筑物抗震设计规范[S].北京:中国计划出版社,1994.GB50191-93,Code for seismic design of structure[J].Beijing:China plan press,1994.
[2]尹海军,徐雷,申跃奎,等.汶川地震中桥梁损伤机理探讨[J].西安建筑科技大学学报:自然科学版,2008,16(5):672-677.YIN Hai-jun,XU Lei,SHEN Yue-kui,et al.Study on the seismic damages to the bridges in Wenchuan Earthquake[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition),2008,16(5):672-677.
[3]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(4):131-136.ZHONG Wan-xie.Precise time-intergration method for structural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131-136.
[4]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,33(1):18-23.LI Qing-ning.The transfer matrix method of bar elements with variable cross-section[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition),2001,5(1):18-23.
[5]李青宁.抛物线连拱精确计算的传递矩阵法[J].西安建筑科技大学学报(自然科学版),1998,20(3):67-70.LI Qing-ning.Transfer matrix method for the accurate calculation of parabolic multi arch[J].J.of Xi′an Univ.of Arch.&Tech.(Natural Science Edition),1998,18(3):67-70.
[6]瞿尔仁,刘孝武,易云焜,等.传递矩阵法在曲线桥结构中的应用[J].合肥工业大学学报:自然科学版,1999,16(6):77-83.QU Er-ren,LI U Xiao-wu,YI Yun-kun,et al.Transfer matrix method applied to structural analysis of curve bridge[J].Journal of Hefei University of Technology(Natural Science Edition),1999,16(6):77-83.
[7]魏双科.曲线梁桥的固有振动特性及地震反应分析[D].南京:南京工业大学,2006.WEI Shuang-ke.Natural dynamic characteristics and seismic response analysis of curved girder bridges[D].Nanjing:Nanjing University of Technology,2006.
[8]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191～195.
[9]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.LI U Qing-tan,NI Guo-rong.The transfer matrix method used in structure analysis[M].Beijing:China Rail way Press,1997.
[10]米彩盈,安琪,李芾.基于传递矩阵法的轮对固有频率计算方法[J].交通运输工程学报,2006,6(4):20-26.MI Cai-ying,AN Qi,LI Fu.Calculation method of wheelset natural frequency based on transfer matrixes[J].Journal of Traffic and Transportation Engineering,2006,6(4):20-26.
[11]GB50191-93,构筑物抗震设计规范[S].北京:中国计划出版社,1994.GB50191-93,Code for seismic design of structure[J].Beijing:China plan press,1994.
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