大质量法在多点激励分析中的应用、误差分析与改进
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摘要
为检验多点激励分析中广泛应用的大质量法(LMM)的计算精度和适用性,基于瑞利阻尼,以2自由度有限元模型为例,在4组不同的地震动输入下,分别用LMM和相对运动法(RMM)进行了多点激励分析。比较了两种方法的结果,从理论上分析了LMM误差产生的原因,指出了LMM的适用条件,进而提出了改进措施——基于地震动输入阻尼项修正(α项修正)的改进LMM,并验证了该方法的精度和适用性。结果表明:采用瑞利阻尼时,LMM会造成不可忽视的误差,理论上不能用于多点激励分析;瑞利阻尼质量比例系数α是导致误差的主要因素,误差大小与α密切相关;改进的LMM可大幅提高计算精度,与RMM结果高度符合,可以满足工程应用。
To verify the practical applicability and accuracy of the large mass method(LMM) widely used in multiple-support seismic excitation analysis of structures,numerical simulations of a two-degrees-of-freedom(2-DOF) finite element model adopting the Rayleigh damping assumption are performed using the LMM and the relative motion method(RMM) respectively under four groups of seismic ground motions.Through comparisons with the RMM,the origin of errors and the applicability of the LMM are discussed.Then the improved LMM is presented herein based on the modification of ground motions considering the influences of Rayleigh damping coefficient α.It indicates that the LMM is not applicable to multi-support excitation analysis in the case of Rayleigh damping,which can cause significant errors.And the errors depend on the damping coefficient α.It is also proved that the improved LMM is able to yield results that are identical to those of the RMM.
To verify the practical applicability and accuracy of the large mass method(LMM) widely used in multiple-support seismic excitation analysis of structures,numerical simulations of a two-degrees-of-freedom(2-DOF) finite element model adopting the Rayleigh damping assumption are performed using the LMM and the relative motion method(RMM) respectively under four groups of seismic ground motions.Through comparisons with the RMM,the origin of errors and the applicability of the LMM are discussed.Then the improved LMM is presented herein based on the modification of ground motions considering the influences of Rayleigh damping coefficient α.It indicates that the LMM is not applicable to multi-support excitation analysis in the case of Rayleigh damping,which can cause significant errors.And the errors depend on the damping coefficient α.It is also proved that the improved LMM is able to yield results that are identical to those of the RMM.
引文
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[2]Leger P,Ide I M,Paultre P.Multiple support seismic analysis of large structures[J].Computers&Structures,1990,36(6):1153―1158.
[3]刘文华,杨庆山.结构多点激励时程分析方法研究[C].第15届全国结构工程学术会议论文集,2006:336―340.Liu Wenhua,Yang Qingshan.Time-history analysis method studies of structure under multi-support excitation[C].Proceedings of the Fifteenth Chinese Symposium on Structural Engineering,2006:336―340.(in Chinese)
[4]于海丰,张耀春.地震动输入方法研究[J].工程力学,2009,26(增刊I):1―6,19.Yu Haifeng,Zhang Yaochun.Discussion on earthquake Input method[J].Engineering Mechanics,2009,26(Sup.I):1―6,19.(in Chinese)
[5]黄小国,胡大琳,张后举.行波效应对大跨度连续刚构桥地震反应的影响[J].长安大学学报(自然科学版),2008,28(1):72―76.Huang Xiaoguo,Hu Dalin,Zhang Houju.Effects of traveling wave to seismic response of long span rigid-framed bridge[J].Journal of Chang’an University(Natural Science Edition),2008,28(1):72―76.(in Chinese)
[6]王有智,夏卫华.用大质量法计算东风EQ140汽车前面罩的强迫运动响应[J].力学与实践,1998,20(5):32―34.Wang Youzhi,Xia Weihua.The calculation of enforced motion response of the front face of dongfeng EQ140truck by large-mass method[J].Mechanics in Engineering,1998,20(5):32―34.(in Chinese)
[7]谢开仲,秦荣,林海瑛.大跨度CFST拱桥地震反应分析方法研究[J].武汉理工大学学报(交通科学与工程版),2005,29(5):700―703.Xie Kaizhong,Qin Rong,Lin Haiying.On methods of seismic response analysis of long-span CFST arch bridge[J].Journal of Wuhan University of Technology(Transportation Science&Engineering),2005,29(5):700―703.(in Chinese)
[8]王田友,丁洁民,楼梦麟.地铁运行所致建筑物振动的传播规律的影响[J].土木工程报,2009,42(5):33―39.Wang Tianyou,Ding Jiemin,Lou Menglin.Subway-Induced building Vibration and Its Propagation[J].China Civil Engineering Journal,2009,42(5):33―39.(in Chinese)
[9]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 Qingshan,Liu Wenhua,Tian Yuji.Response analysis of national stadium under specially variable earthquake ground motions[J].China Civil Engineering Journal,2008,41(2):35―41.(in Chinese)
[10]Clough R W,Ponzien J.Dynamics of structures[M].2nd ed.New York:Computers and Structures,Inc,2004.
[11]胡聿贤.地震工程学[M].第2版.北京:地震出版社,2006.Hu Yuxian.Earthquake engineering[M].2nd ed.Beijing:Earthquake Press,2006.(in Chinese)
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