非比例阻尼线性体系基于规范反应谱的CCQC法
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摘要
根据平稳随机过程理论和抗震设计反应谱,对具有非比例阻尼特性的线性体系,给出了实数形式的复振型反应谱叠加法和复振型完全平方组合(CCQC)计算公式。式中除了包含一般CQC方法中振型间的位移相关系数以外,还包含了新的速度相关系数和位移-速度相关系数。公式推导按照与一般CQC法同样的原理和假定,形式也同样简洁、明了,易于工程设计人员掌握和使用。用实例分析对比了基于设计反应谱的CCQC法、CSRSS法及强迫解耦法,并以人工地震波作为地震输入,用逐步积分法对计算结果进行了验证。结果表明:提出的CCQC法比CSRSS法具有更好的精度。实例分析还表明,对于一般的强非比例阻尼结构,抗震设计规范中采用的强迫解耦方法也具有较好的精度。
A real value form formula of complex mode response superposition method,which is based on the stationary random vibration theory and seismic design spectra,is derived to analysis the non-classically damped linear system.This formula includes new modal velocity correlation coefficient and displacement-velocity cross correlation coefficients besides the modal displacement correlation coefficient in normal Complete Quadratic Combination(CQC) formula.Moreover,the new method has same accuracy and concision as normal CQC method because there is no further assumption involved in it except that have been adopted in normal CQC method.The new proposed CCQC method is easy to master and apply for design engineers.The example analyses and the numerical comparisons with CCQC method,CSRSS method,and the forced uncoupling method proposed by seismic design code are carried out.The results are verified by those obtained from the step-by-step integration method under the simulated man-made seismic wave input.The results demonstrated that CCQC method based on design spectra is more accurate than CSRSS method.Meanwhile,the forced mode uncoupling method widely used in seismic design code also has good approximation,even though the relatively simple example structure is strongly non-proportional.
A real value form formula of complex mode response superposition method,which is based on the stationary random vibration theory and seismic design spectra,is derived to analysis the non-classically damped linear system.This formula includes new modal velocity correlation coefficient and displacement-velocity cross correlation coefficients besides the modal displacement correlation coefficient in normal Complete Quadratic Combination(CQC) formula.Moreover,the new method has same accuracy and concision as normal CQC method because there is no further assumption involved in it except that have been adopted in normal CQC method.The new proposed CCQC method is easy to master and apply for design engineers.The example analyses and the numerical comparisons with CCQC method,CSRSS method,and the forced uncoupling method proposed by seismic design code are carried out.The results are verified by those obtained from the step-by-step integration method under the simulated man-made seismic wave input.The results demonstrated that CCQC method based on design spectra is more accurate than CSRSS method.Meanwhile,the forced mode uncoupling method widely used in seismic design code also has good approximation,even though the relatively simple example structure is strongly non-proportional.
引文
[1]Caughey A K.Classical normal modes in damped linear dynamic systems[J].J.of Applied Mechanics,ASME,1960,27(6):269~271.
[2]Kiureghian A D.Structural response to stationary excitation[J].J.of Engineering Mechanics Division,ASCE,December,1980,106(6):1195~1213.
[3]欧进萍,吴斌,龙旭.耗能减震结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98~107.Ou Jinping,Wu Bin,Long Xu.Aseismic design methods of passive energy dissipation systems[J].Earthq.Eng.and Eng.Vib,1998,18(2):98~107.(in Chinese)
[4]Elishakaff I,Lyon R H.Random vibration-status recent developments[M].Elsvier,1986.
[5]Foss F K.Co-ordinates which uncouple the linear dynamic systems[J].J.of Applied Mechanics,ASME,1958,(24):361~364.
[6]Igusa T,Kiureghian A D,Sackman J L.Modal decomposition method for stationary response of non-classically damped systems[J].Earthq.Eng.Struct.Dyn.,1984,12(1):121~136.
[7]Skinner R I,Robinson,W H and Mcverry G H.An introduction to seismic isolation[M].Jhon Wiley&Sons Ltd,1993.
[8]周锡元.一般有阻尼线性体系地震反应的振型分解方法[M].北京:中国地震工程研究进展,地震出版社,1992.Zhou Xiyuan.The modal superposition method ofearthquake response of general damped linear system[M].Beijing:Published in Research Progress of EarthquakeEngineering in China,(Seismological Press),1992.(inChinese)
[9]周锡元,董娣.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.Zhou Xiyuan,Dong Di.New method for linear systemswith non-classical damping under ground motion[J].China Civil Engineering Journal,2003,36(5):30~36.(inChinese)
[10]Hanson R D,Soong T T.Seismic design withsupplemental energy dissipation devices[M].EERI,NN-8,2001.
[11]GB50011-2001,建筑抗震设计规[S].北京:中国建筑工业出版社,2001.GB50011-2001,Code for seismic design of buildings[S].Beijing:China Architecture and Building Press,2001.(inChinese)
[12]Clough R W,Penzien J.Dynamics of structures[M].Second Edition,McGraw-Hill,Inc,1993.
[13]Tong M,Liang Z,Lee G C.An index of dampingnon-proportionality for discrete vibration system[J].J.ofSound and Vib.,1994,174(1):37~55.
[2]Kiureghian A D.Structural response to stationary excitation[J].J.of Engineering Mechanics Division,ASCE,December,1980,106(6):1195~1213.
[3]欧进萍,吴斌,龙旭.耗能减震结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98~107.Ou Jinping,Wu Bin,Long Xu.Aseismic design methods of passive energy dissipation systems[J].Earthq.Eng.and Eng.Vib,1998,18(2):98~107.(in Chinese)
[4]Elishakaff I,Lyon R H.Random vibration-status recent developments[M].Elsvier,1986.
[5]Foss F K.Co-ordinates which uncouple the linear dynamic systems[J].J.of Applied Mechanics,ASME,1958,(24):361~364.
[6]Igusa T,Kiureghian A D,Sackman J L.Modal decomposition method for stationary response of non-classically damped systems[J].Earthq.Eng.Struct.Dyn.,1984,12(1):121~136.
[7]Skinner R I,Robinson,W H and Mcverry G H.An introduction to seismic isolation[M].Jhon Wiley&Sons Ltd,1993.
[8]周锡元.一般有阻尼线性体系地震反应的振型分解方法[M].北京:中国地震工程研究进展,地震出版社,1992.Zhou Xiyuan.The modal superposition method ofearthquake response of general damped linear system[M].Beijing:Published in Research Progress of EarthquakeEngineering in China,(Seismological Press),1992.(inChinese)
[9]周锡元,董娣.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.Zhou Xiyuan,Dong Di.New method for linear systemswith non-classical damping under ground motion[J].China Civil Engineering Journal,2003,36(5):30~36.(inChinese)
[10]Hanson R D,Soong T T.Seismic design withsupplemental energy dissipation devices[M].EERI,NN-8,2001.
[11]GB50011-2001,建筑抗震设计规[S].北京:中国建筑工业出版社,2001.GB50011-2001,Code for seismic design of buildings[S].Beijing:China Architecture and Building Press,2001.(inChinese)
[12]Clough R W,Penzien J.Dynamics of structures[M].Second Edition,McGraw-Hill,Inc,1993.
[13]Tong M,Liang Z,Lee G C.An index of dampingnon-proportionality for discrete vibration system[J].J.ofSound and Vib.,1994,174(1):37~55.
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