“建桥合一”铁路客站Rayleigh阻尼系数计算方法
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摘要
在显著影响单自由度体系位移方差的激励频率范围内,采用最小二乘法拟合出水平向和竖向地震加速度互功率谱的线性修正表达式,并结合传统随机振动计算方法和规范加速度谱提出了多维激励多阶参考振型Rayleigh阻尼系数计算方法。以"建桥合一"铁路客站天津西站Ⅱ区为工程背景,基于应变能振型阻尼模型求得的结构响应值为标准,对分别基于二阶、单维激励多阶、多维激励多阶参考振型Rayleigh阻尼系数计算方法的结构响应值进行了比较。结果表明:多维激励多阶参考振型Rayleigh阻尼系数计算方法合理考虑了振型和地震激励的相关性,响应值偏差最小,更适合于类似铁路客站Rayleigh阻尼系数的计算。
The linear modified expression of cross power spectrum of seismic acceleration between horizontal and vertical direction was fitted by using least square method in the excitation frequency range that significantly affects the displacement of single freedom system.The calculation method of Rayleigh damping coefficients considering the influence of multidimensional excitations and multi-modes of vibration on behaviors of structure was deduced based on the acceleration spectrum of code,the linear modified expression and the traditional random vibration method.A case study of the Tianjin West Railway Station-Ⅱ,a typical example of integrated building-bridge railway station,was carried out,based on the structural response value obtained from the strain energy proportional damping model,to compare the structural response values based on the deduced method of Rayleigh damping coefficients,the method considering the influence of only two modes and the method considering the influence of singe direction excitation and multi-modes of vibration.The results show that the deviation of structural response value obtained from the deduced method of Rayleigh damping coefficients of multidimensional excitations and multi-modes of vibration is minimal for reasonably considering the correlation of the vibration modes and seismic excitation,and is more suitable for the calculation of Rayleigh damping coefficients of similar integrated building-bridge railway station.
The linear modified expression of cross power spectrum of seismic acceleration between horizontal and vertical direction was fitted by using least square method in the excitation frequency range that significantly affects the displacement of single freedom system.The calculation method of Rayleigh damping coefficients considering the influence of multidimensional excitations and multi-modes of vibration on behaviors of structure was deduced based on the acceleration spectrum of code,the linear modified expression and the traditional random vibration method.A case study of the Tianjin West Railway Station-Ⅱ,a typical example of integrated building-bridge railway station,was carried out,based on the structural response value obtained from the strain energy proportional damping model,to compare the structural response values based on the deduced method of Rayleigh damping coefficients,the method considering the influence of only two modes and the method considering the influence of singe direction excitation and multi-modes of vibration.The results show that the deviation of structural response value obtained from the deduced method of Rayleigh damping coefficients of multidimensional excitations and multi-modes of vibration is minimal for reasonably considering the correlation of the vibration modes and seismic excitation,and is more suitable for the calculation of Rayleigh damping coefficients of similar integrated building-bridge railway station.
引文
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[15]徐汉勇,余志武,李玲瑶.高速铁路客站抗震性能分析的实用虚拟激励法[J].铁道学报,2014,36(9):92-98.XU Hanyong,YU Zhiwu,LI Lingyao.Practical Pseudo Excitation Method for Study of Behavior of High-speed Railway Station under Multiple Earthquake Excitations[J].Journal of the China Railway Society,2014,36(9):92-98.
[2]倪永军,李钊,杨娜,等.“站桥合一”式车站结构抗震性能评估的简化方法[J].振动与冲击,2014,33(5):137-142.NI Yongjun,LI Zhao,YANG Na,et al.Simplified Evaluation Method for Seismic Performance of Integrated Station-Bridge Structures[J].Journal of Vibration and Shock,2014,33(5):137-142.
[3]方联民,朱志辉,王力东,等.车致“站桥合一”高速铁路客站随机振动分析[J].铁道学报,2017,39(9):117-126.FANG Lianmin,ZHU Zhihui,WANG Lidong,et al.Analysis of Train Induced Random Vibration of High-speed Railway Station with“Integral Station-bridge Structure”[J].Journal of the China Railway Society,2017,39(9):117-126.
[4]沈剑波,殷真铭,宴景通,等.上海虹桥火车站主站房结构设计[J].建筑结构,2012,42(9):80-85.SHEN Jianbo,YIN Zhenming,YAN Jingtong,et al.Structural Design on the Main Building of Shanghai Hongqiao Railway Station[J].Building Structure,2012,42(9):80-85.
[5]中华人民共和国住房与城乡建设部.GB 50011—2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.
[6]布占宇,谢旭.不同阻尼计算模式对斜拉桥地震响应分析的影戏[J].中国铁道科学,2006,27(2):46-51.BU Zhanyu,XIE Xu.Effects of Different Damping Modes on the Seismic Response of Cable-stayed Bridges[J].China Railway Science,2006,27(2):46-51.
[7]克拉夫R,彭津J.结构动力学[M].王光远,等译.北京:高等教育出版社,2006.
[8]潘旦光.直接确定Rayleigh阻尼系数的一种优化方法[J].工程力学,2013,30(9):16-21.PAN Danguang.An Optimization Method for the Direct Determination of Rayleigh Damping Coefficients[J].Engineering Mechanics,2013,30(9):16-21.
[9]潘旦光.地震反应分析中Rayleigh阻尼系数的优化解[J].工程力学,2013,30(11):15-20,27.PAN Danguang.An Optimization Solution for Rayleigh Damping Coefficients in Seismic Response Analysis[J].Engineering Mechanics,2013,30(11):15-20,27.
[10]潘旦光,高莉莉.Rayleigh阻尼系数解法比较及对结构地震反应影响[J].工程力学,2015,32(6):192-199.PAN Danguang,GAO Lili.Comparison of Determination Methods for Rayleigh Damping Coefficients and Effects on Seismic Response of Structures[J].Engineering Mechanics,2015,32(6):192-199.
[11]董云,楼梦麟.基于结构基频确定Rayleigh阻尼系数的优化方法及其讨论[J].湖南大学学报,2014,41(2):8-13.DONG Yun,LOU Menglin.An Optimization Solution for Rayleigh Damping Coefficients Based on the Fundamental Frequency of Structure[J].Journal of Hunan University,2017,41(2):8-13.
[12]徐汉勇.新型铁路客站地震响应计算理论研究[D].长沙:中南大学,2015.
[13]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005.
[14]李宏男.结构多维抗震理论[M].北京:科学出版社,2006.
[15]徐汉勇,余志武,李玲瑶.高速铁路客站抗震性能分析的实用虚拟激励法[J].铁道学报,2014,36(9):92-98.XU Hanyong,YU Zhiwu,LI Lingyao.Practical Pseudo Excitation Method for Study of Behavior of High-speed Railway Station under Multiple Earthquake Excitations[J].Journal of the China Railway Society,2014,36(9):92-98.