三维非偏心基础隔震结构非平稳随机振动分析
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摘要
利用虚拟激励法和等效线性化技术,通过缩减等效线性化微分方程的数量,提出了求解三维有限元模型基础隔震结构非平稳随机响应的近似计算方法。计算中,假定隔震系统即使在受到大震激励时,其上部结构也依然处于弹性状态,塑性变形主要集中在隔震层处,隔震支座的本构关系采用Bouc-Wen模型描述。根据基础隔震结构响应的特点,假定同种类型支座相同方向滞迟变量大小相等,这样就可以显著减少参与计算的等效线性化微分方程的数量,降低微分方程组的阶数,提高了计算效率和精度。通过分析一简单的三维基础隔震的框架结构,验证了所提方法的正确性。该方法可以考虑不同类型隔震支座的差异性,方便地求得地震作用下各个支座的破坏情况,对于分析隔震支座在地震中的基础提离问题具有重要意义。
This paper presents a method for evaluating the non-stationary stochastic response of 3D base-isolated buildings by combining the pseudo excitation method and the equivalent linearization method.The analysis is based on the reduction of the number of the equivalent linearization differential equations.It is assumed that the superstructure of the isolation system remains elastic during the earthquakes,even when subjected to major earthquakes;the plastic deformation concentrates in the isolators,of which the relationship between the restoring force and displacement is described by the Bouc-Wen differential equation.The reduction of the number of the equivalent linearization differential equations is achieved by assuming that the hysteretic components of the same type of the isolators are equal to each other in any given directions,which will decrease the order of the differential equations and improve computation accuracy and efficiency.Finally,taking a 3D base-isolated frame structure as an example,the accuracy of the proposed method is verified.The improved method can consider the diversity of the different types of the isolators and obtain the performance of each isolator during the earthquake,which is helpful for evaluating the failure probability by uplift of the isolators.
This paper presents a method for evaluating the non-stationary stochastic response of 3D base-isolated buildings by combining the pseudo excitation method and the equivalent linearization method.The analysis is based on the reduction of the number of the equivalent linearization differential equations.It is assumed that the superstructure of the isolation system remains elastic during the earthquakes,even when subjected to major earthquakes;the plastic deformation concentrates in the isolators,of which the relationship between the restoring force and displacement is described by the Bouc-Wen differential equation.The reduction of the number of the equivalent linearization differential equations is achieved by assuming that the hysteretic components of the same type of the isolators are equal to each other in any given directions,which will decrease the order of the differential equations and improve computation accuracy and efficiency.Finally,taking a 3D base-isolated frame structure as an example,the accuracy of the proposed method is verified.The improved method can consider the diversity of the different types of the isolators and obtain the performance of each isolator during the earthquake,which is helpful for evaluating the failure probability by uplift of the isolators.
引文
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[14]Tena-Colunga A,Zambrana-Rojas C.Dynamic torsionalamplifications of base-isolated structures with eccentricisolation system[J].Engineering Structures,2006,28(1):72―83.
[15]Clough R W,Penzien J.Dynamics of Structures[M].New York:McGraw Hill Book Company,1993:575―612.
[16]Lin J H.A fast algorithm for power spectral of randomseismic responses[J].Earthquake Engineering andEngineering Vibration,1990,10(4):38―46.
[17]Lin J H,Shen W P,Williams F W.Accurate high-speedcomputation of non-stationary random structuralresponse[J].Engineering Structures,1997,19(7):586―593.
[18]张治勇,孙柏涛,宋天舒.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,2000,16(3):33―38.Zhang Zhiyong,Sun Baitao,Song Tianshu.Study on theparameters of seismic power spectrum model based onthe new seismic code[J].World Information onEarthquake Engineering,2000,16(3):33―38.(inChinese)
[19]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1―11.Jiang Jinren,Hong Feng.Conversion between powerspectrum and response spectrum and artificialearthquakes[J].Earthquake Engineering andEngineering Vibration,1984,4(3):1―11.(in Chinese)
[2]Kelly T A.Base isolation of structures:Design guidelines[M].Welington,New Zealand:Holmes ConsultingGroup Ltd,2001:34―57.
[3]Jangid R S,Datta T K.The stochastic response ofasymmetric base isolated buildings[J].Journal of Soundand Vibration,1995,179(3):463―473.
[4]王军,林家浩.剪切型非线性滞迟系统随机地震响应的虚拟激励分析[J].固体力学学报,2001,22(1):23―30.Wang Jun,Lin Jiahao.Seismic random response analysisof non-linear hysteretic systems with pseudo excitationmethod[J].Acta Mechanica Solida Sinica,2001,22(1):23―30.(in Chinese)
[5]杜永峰,李慧,金德保,等.大震下被动与智能隔震结构动力可靠度的对比[J].地震工程与工程振动,2006,26(4):212―219.Du Yongfeng,Li Hui,Jin Debao,et al.Comparison ofseismic reliability of passive and smart isolated structuresunder major earthquake[J].Earthquake Engineering andEngineering Vibration,2006,26(4):212―219.(inChinese)
[6]Pradlwarter H J.Deterministic integration algorithms forstochastic response computations of FE-systems[J].Computers and Structures,2002,80(18/19):1489―1502.
[7]Schu ller G I,Pradlwarter H J,Schenk C A.Nonstationary response of large linear FE-models understochastic loading[J].Computers and Structures,2003,81(8/9/10/11):937―947.
[8]Pradlwarter H J,Schu ller G I,Schenk C A.Acomputational procedure to estimate the stochasticresponse of large non-linear FE-models[J].ComputerMethods in Applied Mechanics and Engineering,2003,192(7/8):777―801.
[9]Wen Y K.Equivalent linearization for hysteretic systemsunder random excitation[J].Journal of AppliedMechanics,1980,47(1):150―154.
[10]Lee D M.Base isolation for torsion reduction inasymmetric structures under earthquake loading[J].Earthquake Engineering and Structural Dynamics,1980,8:349―359.
[11]Pan T C,Kelly J M.Seismic response of torsionallycoupled base isolated structures[J].EarthquakeEngineering and Structural Dynamics,1983,11(6):749―770.
[12]Eisenberger M,Rutenberg A.Seismic base isolation ofasymmetric shear buildings[J].Engineering Structures,1986,8(1):2―8.
[13]Jangid R S,Datta T K.Nonlinear response of torsionallycoupled base isolated structure[J].ASCE Journal ofStructural Engineering,1994,120(1):1―22.
[14]Tena-Colunga A,Zambrana-Rojas C.Dynamic torsionalamplifications of base-isolated structures with eccentricisolation system[J].Engineering Structures,2006,28(1):72―83.
[15]Clough R W,Penzien J.Dynamics of Structures[M].New York:McGraw Hill Book Company,1993:575―612.
[16]Lin J H.A fast algorithm for power spectral of randomseismic responses[J].Earthquake Engineering andEngineering Vibration,1990,10(4):38―46.
[17]Lin J H,Shen W P,Williams F W.Accurate high-speedcomputation of non-stationary random structuralresponse[J].Engineering Structures,1997,19(7):586―593.
[18]张治勇,孙柏涛,宋天舒.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,2000,16(3):33―38.Zhang Zhiyong,Sun Baitao,Song Tianshu.Study on theparameters of seismic power spectrum model based onthe new seismic code[J].World Information onEarthquake Engineering,2000,16(3):33―38.(inChinese)
[19]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1―11.Jiang Jinren,Hong Feng.Conversion between powerspectrum and response spectrum and artificialearthquakes[J].Earthquake Engineering andEngineering Vibration,1984,4(3):1―11.(in Chinese)
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