多跨简支梁桥平稳地震响应分析
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摘要
应用单位脉冲函数,建立了简支梁桥的纵向振动频响函数方程,基于传递函数,提出了用于求解多跨简支梁桥纵向位移和轴力的动态频响函数的计算方法.以六跨简支梁桥为算例,求解了跨中最大位移和轴力,并给出了脉冲荷载作用下相应的傅里叶振幅谱.结果表明,中间各跨跨中位移较大,两侧跨中轴力较大,响应谱的变化规律与位移和轴力的变化一致.
Based on the unit impulse function principle,the frequency response function equation of longitudinal vibration for simply supported beam bridge is established.According to the transfer matrix principle,the calculation method of the dynamic frequency response function for the vertical displacement and axial force of multi-span simply supported beam bridge is proposed.Taking six crosssimply supported girder bridge as an example,the maximum displacement and axial force are solved,and the corresponding Fourier amplitude spectrum under pulse loads is provided.The calculation results show that the mid-pan displacement in the middle of the bridge is bigger than that in the side of the bridge,but the axial force shows an inverse tendency.The changes of the amplitude spectrums are consistent with the displacement and axial force respectively.
Based on the unit impulse function principle,the frequency response function equation of longitudinal vibration for simply supported beam bridge is established.According to the transfer matrix principle,the calculation method of the dynamic frequency response function for the vertical displacement and axial force of multi-span simply supported beam bridge is proposed.Taking six crosssimply supported girder bridge as an example,the maximum displacement and axial force are solved,and the corresponding Fourier amplitude spectrum under pulse loads is provided.The calculation results show that the mid-pan displacement in the middle of the bridge is bigger than that in the side of the bridge,but the axial force shows an inverse tendency.The changes of the amplitude spectrums are consistent with the displacement and axial force respectively.
引文
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[2]谢官模.振动力学[M].北京:国防工业出版社,2007:81-82.XIE Guanmo.Vibration mechanics[M].Beijing:NationalDefense Industry Press,2007:81-82.(in Chinese)
[3]刘建亚,张光明,郑修才.复变函数与积分变换[M].北京:高等教育出版社,2005:154-163.LIU Jianya,ZHANG Guangming,ZHENG Xiucai.Com-plex variables and integral transformation[M].Beijing:Higher Education Press,2005:154-163.(in Chinese)
[4]李志强,张鸿儒,陆传波.挡土结构物随机地震响应分析及动力可靠度研究[J].工程地质学报,2006,14(3):345-350.LI Zhiqiang,ZHANG Hongru,LU Chuanbo.Stochasticanalysis of seismic responses and dynamic reliability of re-taining structures[J].Journal of Engineering Geology,2006,14(3):345-350.(in Chinese)
[5]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998:102-103.OU Jinping,WANG Guangyuan.Random vibration ofstructure[M].Beijing:Higher Education Press,1998:102-103.(in Chinese)
[6]陈兵.桥梁抗震分析的随机理论及应用研究[D].成都:西南交通大学,2008.CHEN Bing.A study on the stochastic theory and applica-tion of bridge seismic analysis[D].Chengdu:SouthwestJiaotong University,2008.(in Chinese)
[7]林家浩,钟万勰,张亚辉.大跨度结构抗震计算的随机振动方法[J].建筑结构学报,2000,21(1):29-35.LIN Jiahao,ZHONG Wanxie,ZHANG Yahui.Seismicanalysis of long span structures by means of random vibra-tion approach[J].Journal of Building Structures,2000,21(1):29-35.(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,2005,38(3):17-22.LIU Xianming,YE Jihong,LI Aiqun.Research of mult-isupport response spectrum method[J].China Civil Eng-ineering Journal,2005,38(3):17-22.(in Chinese)
[9]孙建鹏,李青宁.结构地震反应的频域精细传递矩阵法[J].世界地震工程,2010,26(1):131-136.SUN Jianpeng,LI Qingning.Precise transfer matrixmethod for the earthquake response of structure in frequen-cy domain[J].World Earthquake Engineering,2010,26(1):131-136.(in Chinese)
[10]莫海鸥,王小平.基础工程[M].北京:中国建筑工业出版社,2003:152-153.MO Haiou,WANG Xiaoping.Foundation engineering[M].Beijing:China Architecture&Building Press,2003:152-153.(in Chinese)
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