大跨桥梁地震反应的频域精细传递矩阵法
|
摘要
地震反应分析是研究桥梁抗震能力,指导安全设计的重要手段。大跨度桥梁进行地震反应分析时,需要考虑多点输入影响已成为国内外共识。该文将传递矩阵法与精细积分法的指数矩阵运算相结合,建立了一种精细传递矩阵格式。与传统的传递矩阵法相比,其无需求解微分方程,仅按照迭代公式进行计算,就可得到所需要的传递矩阵。该方法公式简明,规律性强,理论上可实现任意高精度的要求。通过傅里叶变换,推导出了大跨桥梁在一致地震输入和多点地震输入下的频域精细传递矩阵,在频域内对大跨度桥梁进行了动力反应分析。算例表明精细传递矩阵法是正确、有效的。
Seismic response analysis is an important method for studying seismic ability and safe design of bridges.It has been widely accepted that multi-support seismic impact should be considered during the seismic design of the long-span bridges.This paper presents a new transfer matrix format combining the transfer matrix method with the index computing skills of precision integration method.The necessary transfer matrix can be derived following the iterative formula without the need to solve the differential equations.The method' formula is simple but can achieve any high-precision in theory,Based the FFt ransformation,the frequency precise transfer matrix of the long-span bridges under the uniform and multi-support of the earthquake is derived,and the dynamic analysis of the long-span bridges in frequency domain is carried out.The calculation validates the precise transfer matrix method.
Seismic response analysis is an important method for studying seismic ability and safe design of bridges.It has been widely accepted that multi-support seismic impact should be considered during the seismic design of the long-span bridges.This paper presents a new transfer matrix format combining the transfer matrix method with the index computing skills of precision integration method.The necessary transfer matrix can be derived following the iterative formula without the need to solve the differential equations.The method' formula is simple but can achieve any high-precision in theory,Based the FFt ransformation,the frequency precise transfer matrix of the long-span bridges under the uniform and multi-support of the earthquake is derived,and the dynamic analysis of the long-span bridges in frequency domain is carried out.The calculation validates the precise transfer matrix method.
引文
[1]Loh C H,Yeh Y T.Spatial variation and stochastic modeling of seismic differential ground movement[J].Earthquake Eng and Struct Dyn,1988,16(4):583―596.
[2]史志利,李忠献.随机地震动场多点激励下大跨度桥梁地震反应分析方法[J].地震工程与工程振动,2003,21(4):124―130.Shi Zhili,Li Zhongxian.Methods of seismic response analysis for long-span bridges under multi-support excitations of random earthquake ground motion[J].Journal of Earthquake Engineering and Engineering Vibration,2003,21(4):124―130.(in Chinese)
[3]丁阳,张笈玮,李忠献.行波效应对大跨度空间结构随机地震响应的影响[J].地震工程与工程振动,2008,4(1):24―31.Ding Yang,Zhang Jiwei,Li Zhongxian.Influence of wave travelling effect on random seismic responses of long-span spatial structures[J].Journal of Earthquake Engineering and Engineering Vibration,2008,4(1):24―31.(in Chinese)
[4]董刚,朱镜清.结构地震反应分析的频域传递矩阵法[J].计算结构力学及其应用,1994,11(4):429―435.Dong Gang,Zhu Jingqing.Transfer matrix method for the earthquake response of the structure in frequency domain[J].Chinese Journal of Computational Mechanics,1994,11(4):429―435.(in Chinese)
[5]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(2):131―136.Zhong Wanxie.On precise time-intergration method forstructural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131―136.(in Chinese).
[6]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报,2001,5(1):18―23.Li Qingning.The transfer matrix method of bar elements with variable cross-section[J].Journal of Xi’an University of Architecture&Technology,2001,5(1):18―23.(in Chinese)
[7]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191―195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Mechanica Sinica,2004,36(2):191―195.(in Chinese)
[8]刘先明,叶继红,李爱群.多点输入反应谱法的理论研究[J].土木工程学报,2005,4(3):17―22.Liu Xianming,Ye Jihong,Li Aiqun.Research of multisupport response spectrum method[J].China Civil Engineering Journal,2005,4(3):17―22.(in Chinese)
[9]白凤龙.多点输入下大跨结构反应谱分析方法研究进展[J].地震工程与工程振动,2008,6(4):35―42.Bai Fenglong.Advance in research on response spectrum method for seismic analysis of long-span structures[J].Journal of Earthquake Engineering and Engineering Vibration,2008,6(4):35―42.(in Chinese)
[10]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.Zhu Jingqing.Principle of structure seismic analysis[M].Beijing:Earthquake Publishing House,2004.(in Chinese)
[11]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.Liu Qingtan,Ni Guorong.The transfer matrix method used in structure analysis[M].Beijing:China Railway Press,1997.(in Chinese)
[12]李建波.大跨径结构多点激励抗震分析的时频域数值转换算法[J].沈阳建筑大学学报,2007,13(5):756―763.Li Jianbo.Research on numerical conversion algorithms of seismic analysis for long span structure subjected to multi-support excitation in time and frequency domains[J].Journal of Shenyang Jianzhu University,2007,13(5):756―763.(in Chinese)
[2]史志利,李忠献.随机地震动场多点激励下大跨度桥梁地震反应分析方法[J].地震工程与工程振动,2003,21(4):124―130.Shi Zhili,Li Zhongxian.Methods of seismic response analysis for long-span bridges under multi-support excitations of random earthquake ground motion[J].Journal of Earthquake Engineering and Engineering Vibration,2003,21(4):124―130.(in Chinese)
[3]丁阳,张笈玮,李忠献.行波效应对大跨度空间结构随机地震响应的影响[J].地震工程与工程振动,2008,4(1):24―31.Ding Yang,Zhang Jiwei,Li Zhongxian.Influence of wave travelling effect on random seismic responses of long-span spatial structures[J].Journal of Earthquake Engineering and Engineering Vibration,2008,4(1):24―31.(in Chinese)
[4]董刚,朱镜清.结构地震反应分析的频域传递矩阵法[J].计算结构力学及其应用,1994,11(4):429―435.Dong Gang,Zhu Jingqing.Transfer matrix method for the earthquake response of the structure in frequency domain[J].Chinese Journal of Computational Mechanics,1994,11(4):429―435.(in Chinese)
[5]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(2):131―136.Zhong Wanxie.On precise time-intergration method forstructural dynarnics[J].Journal of Dalian University of Technology,1994,34(2):131―136.(in Chinese).
[6]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报,2001,5(1):18―23.Li Qingning.The transfer matrix method of bar elements with variable cross-section[J].Journal of Xi’an University of Architecture&Technology,2001,5(1):18―23.(in Chinese)
[7]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191―195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Mechanica Sinica,2004,36(2):191―195.(in Chinese)
[8]刘先明,叶继红,李爱群.多点输入反应谱法的理论研究[J].土木工程学报,2005,4(3):17―22.Liu Xianming,Ye Jihong,Li Aiqun.Research of multisupport response spectrum method[J].China Civil Engineering Journal,2005,4(3):17―22.(in Chinese)
[9]白凤龙.多点输入下大跨结构反应谱分析方法研究进展[J].地震工程与工程振动,2008,6(4):35―42.Bai Fenglong.Advance in research on response spectrum method for seismic analysis of long-span structures[J].Journal of Earthquake Engineering and Engineering Vibration,2008,6(4):35―42.(in Chinese)
[10]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.Zhu Jingqing.Principle of structure seismic analysis[M].Beijing:Earthquake Publishing House,2004.(in Chinese)
[11]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.Liu Qingtan,Ni Guorong.The transfer matrix method used in structure analysis[M].Beijing:China Railway Press,1997.(in Chinese)
[12]李建波.大跨径结构多点激励抗震分析的时频域数值转换算法[J].沈阳建筑大学学报,2007,13(5):756―763.Li Jianbo.Research on numerical conversion algorithms of seismic analysis for long span structure subjected to multi-support excitation in time and frequency domains[J].Journal of Shenyang Jianzhu University,2007,13(5):756―763.(in Chinese)
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心