相对运动法与绝对位移直接求解法算法误差分析
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摘要
多点激励地震响应分析过程中,相对运动法和绝对位移直接求解法分别假定阻尼与内部节点相对速度、绝对速度成比例,由于阻尼假定的不一致,计算结果可能存在误差。采用随机振动分析方法对瑞利阻尼模型下2种求解方法计算结果之间的误差进行了理论分析,得出了2种算法下结构动态响应功率谱密度误差主要受激励频率与结构基频的比值、结构阻尼比影响的结论,然后从概率统计意义上得出了2种算法下结构动态响应方差误差与结构阻尼比的关系,并进行了相关算例数值论证。最后得出如下结论:2种算法计算结果误差随阻尼比的减小而减小,当结构阻尼比不大于5%时,2种算法计算结果误差基本可忽略。
Under multi-support earthquake excitation,the damping is proportional to the relative velocity in relative motion method,While the damping is proportional to the absolute velocity in method of direct solving absolute displacement,and the damping assuming difference may cause the calculation errors on structural responses.The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model,which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures.Based on probability theory,the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis,and some numerical examples are provided to verify the error analysis.At last,it is pointed out that the calculation errors between the two solving methods decrease with damping ratio,and it is negligible when the damping ratio of structure is less than 5%.
Under multi-support earthquake excitation,the damping is proportional to the relative velocity in relative motion method,While the damping is proportional to the absolute velocity in method of direct solving absolute displacement,and the damping assuming difference may cause the calculation errors on structural responses.The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model,which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures.Based on probability theory,the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis,and some numerical examples are provided to verify the error analysis.At last,it is pointed out that the calculation errors between the two solving methods decrease with damping ratio,and it is negligible when the damping ratio of structure is less than 5%.
引文
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[17]SEVKET ATES,AYDIN DUMANOGLU A,ALEMDARBAYRAKTAR.Stochastic response of seismically isolatedhighway bridges with friction pendulum systems to spatiallyvarying earthquake ground motion[J].EngineeringStructures,2005,27(13):1843-1858.
[2]谢开仲,秦荣,韦立林,等.大跨度CFST拱桥行波效应的地震反应分析[J].桂林工学院学报,2005,25(4):455-459.XIE KAI-ZHONG,QIN RONG,WEI LI-LIN,et al.Seismic response analysis of long span CFST archbridge under the action of traveling waves[J].Journalof Guilin University of Technology,2005,25(4):455-459.
[3]LOU L,ZERVA A.Effects of spatially variableground motions on the seismic response of a skewed,multi-span,RC highway bridge[J].Soil Dynamics andEarthquake Engineering,2005,25(7):729-740.
[4]杨庆山,刘文华,田玉基.国家体育场在多点激励作用下的地震反应分析[J].土木工程学报,2008,41(2):35-41.YANG QING-SHAN,LIU WEN-HUA,TIAN YU-JI.Response analysis of National Stadium underspecially variable earthquake ground motions[J].ChinaCivil Engineering Journal,2008,41(2):35-41.
[5]刘枫,肖从真,徐自国,等.首都机场3号航站楼多维多点输入时程地震反应分析[J].建筑结构学报,2006,27(5):56-63.LIU FENG,XIAO CONG-ZHEN,XU ZI-GUO,et al.Time-history analysis of terminal 3 of the CapitalAirport under multi-support and multi-dimensionseismic excitation[J].Journal of Building Structures,2006,27(5):56-63.
[6]黄明开.非一致激励下大跨空间结构地震反应分析[D].上海:同济大学,2009.
[7]赵灿晖,周志祥.大跨度钢管混凝土拱桥非线性地震响应分析[J].重庆建筑大学学报,2006,28(2):47-51.ZHAO CAN-HUI,ZHOU ZHI-XIANG.Nonlinearseismic response analysis of long-span CFST archbridge[J].Journal of Chongqing Jianzhu University,2006,28(2):47-51.
[8]中华人民共和国交通运输部.JTG/T B02-01-2008公路桥梁抗震设计细则[S].北京:人民交通出版社,2008.
[9]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.
[10]徐培福,傅学怡,王翠坤,等.复杂高层建筑结构设计[M].北京:中国建筑工业出版社,2005.
[11]ZHANG Y H,LI Q S,LIN J H,et al.Randomvibration analysis of long-span structures subjected tospatially varying ground motions[J].Soil Dynamics andEarthquake Engineering,2009,29(4):620-629.
[12]李永华,李思明.绝对位移直接求解的虚拟激励法[J].振动与冲击,2009,28(10):185-190.LI YONG-HUA,LI SI-MING.Pseudo excitation methodbased on solving absolute displacement[J].Journal ofVibration and Shock,2009,28(10):185-190.
[13]胡聿贤.地震工程学[M].2版.北京:地震出版社,2006.
[14]WILSON E L.Static and dynamic analysis of structures:Aphysical approach with emphasis on earthquake engineering[M].Berkley,California:Computers and StructuresInc,2004.
[15]HSIANG-CHUAN TSAI.Modal superposition methodfor dynamic analysis of structures excited by prescribedsupport displacements[J].Computers and Structures,1998,66(5):675-683.
[16]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10.XUE SU-DUO,WANG XUE-SHENG,CAO ZI.Parameters study on seismic random model based on thenew seismic code[J].China Civil Engineering Journal,2003,36(5):5-10.
[17]SEVKET ATES,AYDIN DUMANOGLU A,ALEMDARBAYRAKTAR.Stochastic response of seismically isolatedhighway bridges with friction pendulum systems to spatiallyvarying earthquake ground motion[J].EngineeringStructures,2005,27(13):1843-1858.
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