大刚度法在结构动力分析中的应用、误差分析与改进
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摘要
为检验大刚度法(LSM)的计算精度,以2自由度有限元模型为例,采用瑞利阻尼假设,分别基于一致激励和多点激励情形,输入4组地震动位移,分析了结构的地震反应并与传统理论方法结果做了对比。从理论上分析了LSM误差产生的原因,指出了它的适用条件,分别提出了适用于一致激励和多点激励的改进方法——基于地震动位移阻尼项修正的改进LSM,验证了它们的计算精度。并分析了阻尼系数对LSM和改进LSM的影响。结果表明:采用瑞利阻尼时,理论上LSM不适用于结构地震反应分析;一致激励分析时,LSM的误差与瑞利阻尼的质量相关系数α及刚度相关系数β都有关系,而多点激励分析时误差只与刚度相关系数β密切相关;阻尼系数越大,LSM误差越大,而改进LSM误差很小且表现稳定;改进的LSM可较大幅度提高计算精度,与传统理论方法结果符合精度高。
To verify the practical applicability and accuracy of the large spring/stiffness method(LSM),the dynamic responses of a two-degree-freedom(2DOF) finite element model using the Rayleigh damping assumption are performed respectively according to the LSM and traditional theoretical methods under four groups of seismic ground motion excitations.The origin of errors and the applicability of the LSM are discussed.Then the improved LSM application to a uniform excitation and a non-uniform excitation are respectively presented herein,based on the modification of ground displacements considering the influences of Rayleigh damping.It indicates that the LSM is inapplicable to the structural seismic response analysis in the case of Rayleigh damping theoretically.And the errors depend on the damping coefficients α and β in the case of the uniform seismic excitation and on the coefficient β in the case of the non-uniform seismic excitation respectively.The errors increase monotonously with the aggrandizement of the damping coefficient β.It is also validated that the improved LSM is able to yield results that are identical to those of traditional theoretical methods.
To verify the practical applicability and accuracy of the large spring/stiffness method(LSM),the dynamic responses of a two-degree-freedom(2DOF) finite element model using the Rayleigh damping assumption are performed respectively according to the LSM and traditional theoretical methods under four groups of seismic ground motion excitations.The origin of errors and the applicability of the LSM are discussed.Then the improved LSM application to a uniform excitation and a non-uniform excitation are respectively presented herein,based on the modification of ground displacements considering the influences of Rayleigh damping.It indicates that the LSM is inapplicable to the structural seismic response analysis in the case of Rayleigh damping theoretically.And the errors depend on the damping coefficients α and β in the case of the uniform seismic excitation and on the coefficient β in the case of the non-uniform seismic excitation respectively.The errors increase monotonously with the aggrandizement of the damping coefficient β.It is also validated that the improved LSM is able to yield results that are identical to those of traditional theoretical methods.
引文
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[2]Herting David N.Advanced dynamic analysis,MSC/NASTRAN,User’s guide version 70[M].TheMacNea-Schwendler Corporation,2004.
[3]Wang W,Shi M X.Thick plate theory based on generalsolutions of elasticity[J].Acta Mechanica,1997,123:27―36.
[4]Chen J T,Hong H-K,Yeh C S.Integral representationsand regularizations foe a divergent series solution of abeam subjected to support motions[J].EarthquakeEngineering and Structural Dynamics,1996,25(9):909―925.
[5]Zhou Hongye,Chen Youping.The influence ofphase-difference effects on earthquake response ofcable-stayed bridges[C]//Proceedings of the MSC 1994World User’s Conference,Paper No.37,1994:201―287.
[6]董益亮,郭钢,徐宗俊.道路激励作用下的汽车后桥动力响应分析[J].汽车工程,2002,24(4):339―343.Dong Yiliang,Guo Gang,Xu Zongjun.The Dynamicresponse analysis of the automotive rear axle under roadexcitation[J].Automotive Engineerin,2002,24(4):339―343.(in Chinese)
[7]Clough,Rw Ponzien J.Dynamics of structures[M].2nded.New York:Computers and Structures,Inc,2004.
[8]周国良,李小军,喻畑.结构地震作用的基底激励模型及其适用性[J].建筑结构学报,2010,31(增刊2):82―88.Zhou Guoliang,Li Xiaojun,Yu Tian.Applicabilityresearch on base excitation models used in structuralseismic response analysis[J].Journal of BuildingStructures,2010,31(Sup.2):82―88.(in Chinese)
[9]Zhou Guoliang,Li Xiaojun.Improved large mass methodfor structural base excitation analysis[J].AppliedMechanics and Materials,2010,29-32(2010):1588―1593.
[10]Edward L Wilson.Three-dimensional static and dynamicanalysis of structures[M].3rd ed.UC.Berkeley:Computers and Structures,Inc,2002.
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