多层隔震结构近似实空间解耦及地震作用取值
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摘要
为研究多层非经典阻尼隔震结构响应及其地震作用取值,首先建立了多层隔震结构响应近似实空间解耦分析法,并基于随机振动理论将结构位移随机响应方差解析分解为系列标准振子的位移与速度随机响应方差的线性组合;然后利用系列标准振子最大响应与反应谱的对应关系,建立了多层隔震结构基于抗震规范加速度反应谱的位移最大响应及其等效静态地震作用取值的近似解析分析法,并给出算例。采用本文方法计算的结构位移时程分析、位移响应方差和层间剪力设计值的最大误差分别仅为0.392 8%、0.020 6%和0.079 9%,结果表明该方法简便实用,精度较高,可用于工程实际。
In order to study the seismic response of multistory isolated non-classical damping structures,the response equations with damping and symmetric mass matrix were established by the method of approximate decouping in real spaces.Then,by the random vibration theory,the meansquare values of structural displacement random response are decomposed to a linear combination of mean-square values of displacement and velocity random response of serial standard oscillators.Lastly,according to the relationship between the maximum displacement response of serial standard oscillators and response spectrum,the analytic solution of maximum displacement response and earthquake action of the isolated structures based on response spectrum are obtained.The proposed method was used to calculate the displacement time history,the mean-square value of displacement response and the design value of interlaminar shear force,the maximum errors of which are only 0.392 8%,0.020 6% and 0.079 9%,respectively.The result shows that this method is simple,practical,and accurate.
In order to study the seismic response of multistory isolated non-classical damping structures,the response equations with damping and symmetric mass matrix were established by the method of approximate decouping in real spaces.Then,by the random vibration theory,the meansquare values of structural displacement random response are decomposed to a linear combination of mean-square values of displacement and velocity random response of serial standard oscillators.Lastly,according to the relationship between the maximum displacement response of serial standard oscillators and response spectrum,the analytic solution of maximum displacement response and earthquake action of the isolated structures based on response spectrum are obtained.The proposed method was used to calculate the displacement time history,the mean-square value of displacement response and the design value of interlaminar shear force,the maximum errors of which are only 0.392 8%,0.020 6% and 0.079 9%,respectively.The result shows that this method is simple,practical,and accurate.
引文
[1]中华人民共和国住房和城乡建设部.GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.
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[3]李暾,李创第.带TMD高层结构抗风优化设计[J].广西大学学报:自然科学版,2009,10(5):595-598.
[4]李创第,葛新广,朱倍权.带五种被动减震器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,26(4):144-152.
[5]黄东梅,李创第,陈俊忠.基础隔震结构基于反应谱的地震作用取值[J].西安建筑科技大学学报,2007,39(4):504-511.
[6]周锡元,董娣,苏幼坡.非正交阻尼线性系统的复振型地震响应叠加分析法[J].土木工程学报,2003,36(5):30-36.
[7]闫维明.非正交阻尼体系地震反应的非经典反应谱反应谱方法[J].华南建设学院学报,1995,5(2):9-14.
[8]崔峰,蒋永生,刘文峰.基于反应谱理论的复模态抗震设计方法[J].地震工程与工程振动,2002,22(3):32-36.
[9]HWANG T S,CHANG K C,TSAI M H.Composite damping ratio of seismically isolated regular bridge[J].EngineeringStructures,1997,19(1):52-62.
[10]李中锡,周锡元.规则型隔震房屋的自振特性和地震反应分析方法[J].地震工程与工程振动,2002,22(2):33-41.
[11]付伟庆,刘文光,王建,等.高层隔震结构的等效简化模型研究[J].地震工程与工程振动,2005,25(16):141-145.
[12]王焕定,付伟庆,刘文光,等.规则隔震结构等效简化模型的研究[J].工程力学,2006,23(8):138-143.
[13]潘东辉,于国有,张德强.隔震高层结构的悬臂梁模型的地震反应研究[J].工程力学,2012,29(5):115-211.
[14]HWANG J H,MA F.On the approximate solution of nonclassically damped linear systems[J].Journal of Applied Me-chanics,1993,60:695-701.
[15]欧进萍,刘会仪.基于随机地震动模型的结构随机地震反应谱及其应用[J].地震工程与工程振动,1994,14(1):14-22.
[16]LIN Y Y,CHANG K C.Study on damping reduction factor for buildings under earthquake ground motions[J].Journal ofStructural Engineering,2003,129(2):206-214.
[2]王亚勇,郭子雄,吕西林.建筑抗震设计中的地震作用取值—主要国家抗震规范比较[J].建筑科学,1999,15(5):36-39.
[3]李暾,李创第.带TMD高层结构抗风优化设计[J].广西大学学报:自然科学版,2009,10(5):595-598.
[4]李创第,葛新广,朱倍权.带五种被动减震器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,26(4):144-152.
[5]黄东梅,李创第,陈俊忠.基础隔震结构基于反应谱的地震作用取值[J].西安建筑科技大学学报,2007,39(4):504-511.
[6]周锡元,董娣,苏幼坡.非正交阻尼线性系统的复振型地震响应叠加分析法[J].土木工程学报,2003,36(5):30-36.
[7]闫维明.非正交阻尼体系地震反应的非经典反应谱反应谱方法[J].华南建设学院学报,1995,5(2):9-14.
[8]崔峰,蒋永生,刘文峰.基于反应谱理论的复模态抗震设计方法[J].地震工程与工程振动,2002,22(3):32-36.
[9]HWANG T S,CHANG K C,TSAI M H.Composite damping ratio of seismically isolated regular bridge[J].EngineeringStructures,1997,19(1):52-62.
[10]李中锡,周锡元.规则型隔震房屋的自振特性和地震反应分析方法[J].地震工程与工程振动,2002,22(2):33-41.
[11]付伟庆,刘文光,王建,等.高层隔震结构的等效简化模型研究[J].地震工程与工程振动,2005,25(16):141-145.
[12]王焕定,付伟庆,刘文光,等.规则隔震结构等效简化模型的研究[J].工程力学,2006,23(8):138-143.
[13]潘东辉,于国有,张德强.隔震高层结构的悬臂梁模型的地震反应研究[J].工程力学,2012,29(5):115-211.
[14]HWANG J H,MA F.On the approximate solution of nonclassically damped linear systems[J].Journal of Applied Me-chanics,1993,60:695-701.
[15]欧进萍,刘会仪.基于随机地震动模型的结构随机地震反应谱及其应用[J].地震工程与工程振动,1994,14(1):14-22.
[16]LIN Y Y,CHANG K C.Study on damping reduction factor for buildings under earthquake ground motions[J].Journal ofStructural Engineering,2003,129(2):206-214.
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