多点地震输入下结构地震反应分析的频域精细传递矩阵法
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摘要
正确的地震输入方式是研究工程结构抗震性能的首要因素。结构的地震反应分析,需要考虑多点地震输入的影响。将精细传递矩阵理论与拟静力原理相结合,建立多点地震输入下结构地震反应分析的频域精细传递矩阵法。首先,根据梁单元的几何物理关系,建立梁单元的状态传递矩阵;其次,根据傅里叶变换,建立集中质量两侧的状态传递矩阵;然后,根据转折处及分支点处的结构特点,建立转折处及分支点处的状态传递矩阵;最后,根据结构的实际特点,建立结构总的传递矩阵。在上述算法的基础上,编制了计算程序,并进行了相应的算例计算。算例计算结果表明,结构在水平方向地震力的作用下,边柱的地震反应考虑一致激励较为合理;中柱水平方向考虑一致激励较为合理,而竖直方向应考虑多点激励的不利影响。
The appropriate method for considering earthquake input is of most importance in seismic analysis of structures.The effects of multi-support excitations should be considered in earthquake response analysis of structures.In this paper,under the combination of refined transfer matrix theory and pseudo-static theorem,precise frequency domain transfer matrix method for structure seismic response analysis under multi-support excitation was developed.First,based on the relationship between geometry and physics of beam element,the state transition matrix of beam element was built.And then,based on the feature of structure hinge part and branch point,the state transition matrixes of hinge part and branch point were built.Finally,according to the actual characteristics of a structure,the total transfer matrix was derived.Such algorithm was compiled in a computational procedure a numerical example was exhibited.The results show that,under the horizontal seismic force,the edge columns should be considered for the uniform excitation in both the horizontal and the vertical directions.For middle columns,the uniform excitation is reasonable in seismic response analysis,however,the disadvantage effects of multi-support excitations should be considered in vertical direction.
The appropriate method for considering earthquake input is of most importance in seismic analysis of structures.The effects of multi-support excitations should be considered in earthquake response analysis of structures.In this paper,under the combination of refined transfer matrix theory and pseudo-static theorem,precise frequency domain transfer matrix method for structure seismic response analysis under multi-support excitation was developed.First,based on the relationship between geometry and physics of beam element,the state transition matrix of beam element was built.And then,based on the feature of structure hinge part and branch point,the state transition matrixes of hinge part and branch point were built.Finally,according to the actual characteristics of a structure,the total transfer matrix was derived.Such algorithm was compiled in a computational procedure a numerical example was exhibited.The results show that,under the horizontal seismic force,the edge columns should be considered for the uniform excitation in both the horizontal and the vertical directions.For middle columns,the uniform excitation is reasonable in seismic response analysis,however,the disadvantage effects of multi-support excitations should be considered in vertical direction.
引文
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[9]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.(LiuXianming,Ye Jihong,Li Aiqun.Research ofmultisupport response spectrum method[J].China CivilEngineering Journal,2005,38(3):17-22.(inChinese))
[10]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.
[11]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,33(1):18-23.(LiQingning.The transfer matrix method of bar elementswith variable cross-section[J].Journal of Xi’anUniversity of Architecture&Technology:NaturalScience Edition,2001,33(1):18-23.(in Chinese))
[12]孙建鹏,李青宁.求解结构自振频率的精细传递矩阵法[J].世界地震工程,2009,25(2):140-145.(SunJianpeng,Li Qingning.Precise transfer matrix methodfor resolving natural frequencies of structures[J].WorldEarthquake Engineering,2009,25(2):140-145.(inChinese))
[13]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.
[2]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.
[3]史志利,李忠献.随机地震动场多点激励下大跨度桥梁地震反应分析方法[J].地震工程与工程振动,2003,23(4):124-130.(SHI Zhili,LI Zhongxian.Methods of seismic response analysis for long-spanbridges under multi-support excitations of randomearthquake ground motion[J].Journal of EarthquakeEngineering and Engineering Vibration,2003,23(4):124-130.(in Chinese))
[4]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析[J].地震工程与工程振动,2003,23(2):68-76.(LI Zhongxian.SHI Zhili,Seismicresponse analysis for long-span continuous rigid-framedbridges under excitation of traveling waves[J].Journalof Earthquake Engineering and Engineering Vibration,2003,23(2):68-76.(in Chinese))
[5]董刚,朱镜清.结构地震反应分析的频域传递矩阵法[J].计算结构力学及其应用,1994,11(4):429-435.(Dong Gang,Zhu Jingqing.Transfer matrix method forthe earthquake response of the structure in frequencydomain[J].Chinese Journal of ComputationalMechanics 1994,11(4):429-435.(in Chinese))
[6]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,2(2):131-136.(Zhong Wanxie.On precise time-integration method for structuraldynamics[J].Journal of Dalian University ofTechnology,1994,2(2):131-136.(in Chinese))
[7]刘天云,刘光廷,薛颖.地震多点激励结构随机分析方法[J].世界地震工程,2001,17(4):88-92.(LiuTianyun,Liu Guangting,Xue Ying.A random analyticalapproach for structures with random multi-pointearthquake exciation[J].World EarthquakeEngineering,2001,17(4):88-92.(in Chinese))
[8]陈健云,林皋.多点输入随机地震动拱坝一地基体系反应分析[J]世界地震工程,2000,16(3):39-43.(Chen Jianyun,Lin Gao.Random response analysis ofarch dam-foundation system subjected to multi-inputseismic excitation[J].World Earthquake Engineering,2000,16(3):39-43.(in Chinese))
[9]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.(LiuXianming,Ye Jihong,Li Aiqun.Research ofmultisupport response spectrum method[J].China CivilEngineering Journal,2005,38(3):17-22.(inChinese))
[10]朱镜清.结构抗震分析原理[M].北京:地震出版社,2004.
[11]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,33(1):18-23.(LiQingning.The transfer matrix method of bar elementswith variable cross-section[J].Journal of Xi’anUniversity of Architecture&Technology:NaturalScience Edition,2001,33(1):18-23.(in Chinese))
[12]孙建鹏,李青宁.求解结构自振频率的精细传递矩阵法[J].世界地震工程,2009,25(2):140-145.(SunJianpeng,Li Qingning.Precise transfer matrix methodfor resolving natural frequencies of structures[J].WorldEarthquake Engineering,2009,25(2):140-145.(inChinese))
[13]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.
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