非比例阻尼隔震结构地震响应的实振型分解法
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摘要
采用子结构瑞利阻尼模型表达隔震体系的非比例阻尼矩阵,将实振型分解法与拉普拉斯变换方法联合应用,建立了任意多自由度非比例阻尼隔震体系时域动力响应的工程算法。以本文作者承担设计的三个实际隔震工程作为算例,在两种不同输入地震波和三种不同隔震层阻尼水准下,用本文算法计算地震响应,并与复振型分解法、Wilson-θ法、及Matlab下的Simulink这三种方法的峰值响应进行了对比。结果表明,在设计阻尼水准(隔震层阻尼比为0.21)下,本文算法与Wilson-θ算法的精度大致相当,所求得的位移、速度及加速度峰值的最大相对误差分别不超过0.07%、0.19%和0.27%。即使在极大阻尼水准(隔震阻尼比为0.81)下,本文算法所求得的所有峰值响应的最大相对误差均不超过4%。这表明,当隔震阻尼比不是特别大时,本文提出的算法完全可以满足工程计算要求。
An approximate method for analyzing seismic response of non-proportionally damped base isolated structures in time domain is derived by combining real mode superposition and Laplace transform method. The non-proportional damping matrix is expressed in the form of sub structural Rayleigh damping model. Three of the isolated buildings which were designed by the authors have been used as numerical examples, inputting two different earthquake waves under 3 different isolation damping levels. A comparison of calculated results is made with complex modal superposition, the Wilson-θmethod coded in double precision Fortran, and the Simulink method in Matlab. It is shown that under the design damping level defined in this paper, i.e., the isolation damping ratio is 0.21, the result of the present method is basically as accurate as the Wilson-θmethod, and the maximum relative errors of the peak displacement, velocity and acceleration are less than 0.07%, 0.19% and 0.27%, respectively, of their maximum response. Even if under an extremely heavy damping level (isolation damping ratio 0.81), the maximum relative errors of all peak responses of interest are still less than 4%, indicating that the method presented in this paper is sufficiently accurate for use in engineering analysis.
An approximate method for analyzing seismic response of non-proportionally damped base isolated structures in time domain is derived by combining real mode superposition and Laplace transform method. The non-proportional damping matrix is expressed in the form of sub structural Rayleigh damping model. Three of the isolated buildings which were designed by the authors have been used as numerical examples, inputting two different earthquake waves under 3 different isolation damping levels. A comparison of calculated results is made with complex modal superposition, the Wilson-θmethod coded in double precision Fortran, and the Simulink method in Matlab. It is shown that under the design damping level defined in this paper, i.e., the isolation damping ratio is 0.21, the result of the present method is basically as accurate as the Wilson-θmethod, and the maximum relative errors of the peak displacement, velocity and acceleration are less than 0.07%, 0.19% and 0.27%, respectively, of their maximum response. Even if under an extremely heavy damping level (isolation damping ratio 0.81), the maximum relative errors of all peak responses of interest are still less than 4%, indicating that the method presented in this paper is sufficiently accurate for use in engineering analysis.
引文
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[10]J M Kelly.The role of damping in seismic isolation[J].Earthq.Engrg.andStruc.Dyn.1999,28(1):3-20.
[11]杜永峰,杜小妮,赵国藩.用拉普拉斯变换方法求解非比例阻尼隔震结构[J].兰州大学学报(自然科学版),2000,36(11):40-45.DuYongfeng,DuXiaoni,ZhaoGuofan.Calculation of non-proportionally damped isolated structures usingLaplace transform method[J].Journal ofLanzhouUniversity(NaturalScience),2000,36(11):40-45.(inChinese)
[12]CloughR W andPenzienJ.Dynamics of strctures[M].2nd ed.NewYork:McGraw-Hill,1993.
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[14]SinhaR andIgusaT.CQC andSRSS method for non-classically damped structures[J].EarthqEngrg andStrucDyn,1990,24(4):615-619.
[15]DuYongfeng,LiHui andSpencerBillieF Jr.Effect ofNon-ProportionalDamping onSeismicIsolation[J].Journal ofStructuralControl,2002,9(3):205-236.
[16]杜永峰,李慧,SpencerB F Jr,等.隔震结构动力时程响应的一种工程实用算法[J].甘肃工业大学学报,2003,29(3):70-75.DuYongfeng,LiHui,SpencerB F Jr, et al.A practical engineering method for calculating time domain response of isolated buildings[J].Journal ofGansuUniversity ofTechnology,2003,29(3):70-75.(inChinese)
[2]MauS T.A subspace modal superposition method for non-classically damped systems[J].EarthquakeEng.Struct.Dyn.,1988,16:931-942.
[3]VeletsosA S andVenturaC E.Modal analysis of non-classically damped linear systems[J].EarthquakeEng.Struct.Dyn.,1986,14:217-243.
[4]D扐veniA andMuscolinoG.Improved dynamic correction method in seismic analysis of both classicallyand non- classically damped structures[J].Earthq.Engrg. andStruc.Dyn.,2001,30(4):501-517.
[5]SpencerB F Jr,JohnsonE A andRamalloJ C.揝mart?isolation for seismic control[J].JSME InternationalJournal,Special issue on揊rontiers ofMotion andVibrationControl.?000,SeriesC,43(3):704-711.
[6]秦权,楼磊.非经典阻尼对悬索桥地震反应的影响[J].土木工程学报,1999,32(3):17-22.QinQuan,LouLei.Effect of non-proportional damping on seismic responses of suspension bridges[J].ChinaCivilEngineeringJournal,1999,32(3):17-22.
[7]ClaretA M andVenancio-FilhoF.A modal superposition pseudo-force method for dynamic analysis of structural systems with non-proportional damping[J].EarthquakeEng.Struct.Dyn.1991,20:303-315.
[8]郭永刚,曲乃泗,董毓新.非比例阻尼对结构动力响应影响的摄动分析方法[J].地震工程与工程振动,1995,15(4):48-54.GuoYonggang,QuNaisi,DongYuxin.Perturbation analysis method of the non-proportional damping effect on structure dynamic response[J].EarthquakeEngineering andEngineeringVibration,1995,15(4):48-54.(inChinese)
[9]周锡元.一般有阻尼线性体系地震反应的振型分解方法[A].国家地震局工程力学研究所主编.地震工程研究进展(刘恢先80寿辰纪念文集)[C].北京:地震出版社,1992.120-125.ZhouXiyuan.Mode superposition method for calculating seismic response of generally damped linear systems[A].Institute ofEngineeringMechanics,ChinaSeismologicalBureau(eds).Advances inEarthquakeEngineeringResearch(Collection in honor of80th birth day ofProfLiu,H.X.)[C].Beijing:SeismologyPress,1992.120-125.(inChinese)
[10]J M Kelly.The role of damping in seismic isolation[J].Earthq.Engrg.andStruc.Dyn.1999,28(1):3-20.
[11]杜永峰,杜小妮,赵国藩.用拉普拉斯变换方法求解非比例阻尼隔震结构[J].兰州大学学报(自然科学版),2000,36(11):40-45.DuYongfeng,DuXiaoni,ZhaoGuofan.Calculation of non-proportionally damped isolated structures usingLaplace transform method[J].Journal ofLanzhouUniversity(NaturalScience),2000,36(11):40-45.(inChinese)
[12]CloughR W andPenzienJ.Dynamics of strctures[M].2nd ed.NewYork:McGraw-Hill,1993.
[13]WarburtonG B andSoniS R.Errors in response calculations for non-classically damped structures[J].EarthqEngrg andStrucDyn,1977,5(2):365-376.
[14]SinhaR andIgusaT.CQC andSRSS method for non-classically damped structures[J].EarthqEngrg andStrucDyn,1990,24(4):615-619.
[15]DuYongfeng,LiHui andSpencerBillieF Jr.Effect ofNon-ProportionalDamping onSeismicIsolation[J].Journal ofStructuralControl,2002,9(3):205-236.
[16]杜永峰,李慧,SpencerB F Jr,等.隔震结构动力时程响应的一种工程实用算法[J].甘肃工业大学学报,2003,29(3):70-75.DuYongfeng,LiHui,SpencerB F Jr, et al.A practical engineering method for calculating time domain response of isolated buildings[J].Journal ofGansuUniversity ofTechnology,2003,29(3):70-75.(inChinese)
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