基于粘性阻尼假定的反应谱CCQC法研究
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摘要
采用虚拟激励法推导出基于粘性阻尼假定和任意平稳随机地震动的复振型完全平方组合(CCQC)法原始表达式(OCCQC)及其传统简化表达式TCCQC,并与基于复阻尼假定的平稳随机振动分析结果进行对比。结果表明:高厚比较大的结构TCCQC式计算结果偏小较多,而OCCQC式计算结果更加接近,比TCCQC式要更为合理;基于粘性阻尼假定时,阻尼矩阵与复模态分析结果之间相互影响,反应谱CCQC法计算结果不惟一,合理性不易被判定;若粘性阻尼矩阵构造得当,反应谱CCQC法计算结果与基于复阻尼假定的平稳随机振动分析结果接近,但要构造恰当的粘性阻尼矩阵费时费力;结构设置有粘性阻尼类型机械阻尼器时宜采用基于粘性阻尼假定的反应谱CCQC法,否则采用基于复阻尼假定的反应谱CCQC法更加便捷。
A pseudo-excitation method was used to deduce a new formula of original complex complete quadratic combination(OCCQC) method and its simplified form according to traditionally simplified complex complete quadratic combination(TCCQC).The results of TCCQC were compared with the results of stationary random vibration analysis based on complex damping assumption.The results show that the results of TCCQC of structures which have greater height to thickness ratio are much less,while the calculation results of OCCQC are in good agreement,which shows that OCCQC is more rational than TCCQC.Damping matrix based on viscous damping assumption interacts with results of complex modal analysis,so calculation results of response spectrum CCQC method are not unique and the rationality of results is difficult to be determined.If viscous damping matrix is properly constructed,calculation results of the response spectrum CCQC method based on viscous damping assumption will agree well with that of stationary random vibration analysis based on complex damping assumption,but constructing proper viscous damping matrix is a time-consuming and hard work.The response spectrum CCQC method based on viscous damping assumption is suggested only for structures where viscous damping type mechanical dampers are placed,otherwise the response spectrum CCQC method based on complex damping assumption is more convenient and efficient.
A pseudo-excitation method was used to deduce a new formula of original complex complete quadratic combination(OCCQC) method and its simplified form according to traditionally simplified complex complete quadratic combination(TCCQC).The results of TCCQC were compared with the results of stationary random vibration analysis based on complex damping assumption.The results show that the results of TCCQC of structures which have greater height to thickness ratio are much less,while the calculation results of OCCQC are in good agreement,which shows that OCCQC is more rational than TCCQC.Damping matrix based on viscous damping assumption interacts with results of complex modal analysis,so calculation results of response spectrum CCQC method are not unique and the rationality of results is difficult to be determined.If viscous damping matrix is properly constructed,calculation results of the response spectrum CCQC method based on viscous damping assumption will agree well with that of stationary random vibration analysis based on complex damping assumption,but constructing proper viscous damping matrix is a time-consuming and hard work.The response spectrum CCQC method based on viscous damping assumption is suggested only for structures where viscous damping type mechanical dampers are placed,otherwise the response spectrum CCQC method based on complex damping assumption is more convenient and efficient.
引文
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[2]周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程学报,2003,36(5):30-36,45.ZHOU Xi-yuan,DONG Di,SU You-po.New Methodfor Linear Systems with Non-classical DampingUnder Ground Motion[J].China Civil EngineeringJournal,2003,36(5):30-36,45.
[3]ZHOU X Y,YU R F,DONG D.Complex ModeSuperposition Algorithm for Seismic Responses ofNon-classically Damped Linear MDOF System[J].Journal of Earthquake Engineering,2004,8(4):597-641.
[4]周锡元,马东辉,俞瑞芳.工程结构中的阻尼与复振型地震响应的完全平方组合[J].土木工程学报,2005,38(1):31-39.ZHOU Xi-yuan,MA Dong-hui,YU Rui-fang.Damp-ing in Structures and Complete Quadratic Combina-tion(CCQC)of Complex Mode Seismic Responses[J].China Civil Engineering Journal,2005,38(1):31-39.
[5]周锡元,俞瑞芳.非比例阻尼线性体系基于规范反应谱的CCQC法[J].工程力学,2006,23(2):10-17,9.ZHOU Xi-yuan,YU Rui-fang.CCQC Method forSeismic Response of Non-classically Damped LinearSystem Based on Code Response Spectra[J].Engin-eering Mechanics,2006,23(2):10-17,9.
[6]俞瑞芳,周锡元.具有过阻尼特性的非比例阻尼线性系统的复振型分解法[J].建筑结构学报,2006,27(1):50-59.YU Rui-fang,ZHOU Xi-yuan.Complex Mode Super-position Method for Non-classically Damped LinearSystem with Over-critical Damping Peculiarity[J].Journal of Building Structures,2006,27(1):50-59.
[7]DER KIUREGHIAN A.A Response Spectrum Methodfor Random Vibration Analysis of MDF Systems[J].Earthquake Engineering and Structural Dynamics,1981,9(5):419-435.
[8]CLOUGH R W,PENZIEN J.Dynamics of Structures[M].2nd ed.Berkeley:Computers and Structures,Inc.,2003.
[9]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005.LIU Jing-bo,DU Xiu-li.Dynamics of Structures[M].Beijing:China Machine Press,2005.
[10]DER KIUREGHIAN A.Structural Response to Sta-tionary Excitation[J].Journal of the EngineeringMechanics Division,1980,106(6):1195-1213.
[11]DER KIUREGHIAN A,NAKAMURA Y.CQCModal Combination Rule for High-frequency Modes[J].Earthquake Engineering and Structural Dynam-ics,1993,22(11):943-956.
[12]CACCIOLA P,COLAJANNI P,MUSCOLINO G.Combination of Modal Responses Consistent withSeismic Input Representation[J].Journal of Struc-tural Engineering,2004,130(1):47-55.
[13]刘庆林,傅学怡.基于复阻尼假定的不同材料阻尼特性混合结构抗震分析反应谱CCQC法[J].土木工程学报,2011,44(3):61-71.LIU Qing-lin,FU Xue-yi.A Response SpectrumCCQC Method for Seismic Analysis of Structures ofMultiple Material Damping Characteristics Based onComplex Damping Assumption[J].China Civil Engin-eering Journal,2011,44(3):61-71.
[14]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.LIN Jia-hao,ZHANG Ya-hui.Pseudo-excitationMethod for Random Vibration[M].Beijing:SciencePress,2004.
[15]傅学怡.国家游泳中心水立方结构设计[M].北京:中国建筑工业出版社,2009.FU Xue-yi.Structural Design of National SwimmingCentre Water Cube[M].Beijing:China Architecture&Building Press,2009.
[16]邱吉宝,向树红,张正平.计算结构动力学[M].合肥:中国科学技术大学出版社,2009.QIU Ji-bao,XIANG Shu-hong,ZHANG Zheng-ping.Computational Structural Dynamics[M].Hefei:Uni-versity of Science and Technology of China Press,2009.
[17]孙景江,江近仁.与规范反应谱相对应的金井清谱的谱参数[J].世界地震工程,1990,8(1):42-48.SUN Jing-jiang,JIANG Jin-ren.Parameters of Kanai-Tajimi Spectrum Consistent with State Code[J].World Earthquake Engineering,1990,8(1):42-48.
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