带支撑分数导数粘滞阻尼器减震结构随机响应
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摘要
对带支撑分数粘滞阻尼器单自由度耗能结构的随机地震响应与等效阻尼进行了系统研究。首先,建立结构运动方程;然后应用随机平均法,将结构响应幅值近似为扩散过程,获得了结构位移与速度联合概率密度函数以及位移、速度响应方差的解析解;最后,基于随机平均分析完全相同的等效准则,建立了可直接应用反应谱法的上述阻尼器的等效阻尼计算公式,给出了算例,并分析了所得公式的合理性。
The random earthquake response and equivalent damping of SDOF dissipation structure with the supporting brace and the in-line viscous dampers based on the fractional derivative model were studied systematically.The dynamic equations of the structure were established.Then,employing the stochastic averaging method,the structural amplitude diffusion was obtained,and the exact solutions of joint probability density function and mean-square values of structural displacement and velocity were given.Finally,using the equivalent criterion of stochastic averaging analysis,the analytic formulas of equivalent damping of the viscous dampers based on the fractional derivative model with supporting brace were established,which makes it possible to use the response spectrum in structures.An example using these methods was given.
The random earthquake response and equivalent damping of SDOF dissipation structure with the supporting brace and the in-line viscous dampers based on the fractional derivative model were studied systematically.The dynamic equations of the structure were established.Then,employing the stochastic averaging method,the structural amplitude diffusion was obtained,and the exact solutions of joint probability density function and mean-square values of structural displacement and velocity were given.Finally,using the equivalent criterion of stochastic averaging analysis,the analytic formulas of equivalent damping of the viscous dampers based on the fractional derivative model with supporting brace were established,which makes it possible to use the response spectrum in structures.An example using these methods was given.
引文
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[2]SOONG TT,DARGUSHG F.Passive energy dissipation systems in structural engineering[M].England:John Wiley andSons Ltd,1997.
[3]杨仕升,郝效强,秦荣.钢筋混凝土结构薄弱环节与抗震加固分析研究[J].广西大学学报:自然科学版,2008,33(3):211-215.
[4]瞿伟廉.高层建筑和高耸结构的风振控制设计[M].武汉:武汉测绘科技大学出版社,1991.
[5]欧进萍,吴斌,龙旭.耗能减振结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98-107.
[6]李创第,葛新广.带五种被动减振器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,33(4):144-152.
[7]李创第,黄天立.TMD控制优化设计与振动台试验研究[J].土木工程学报,2006,33(7):19-25.
[8]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[9]周锡元,阎淮明,杨润林.建筑结构的隔震、减震和振动控制[J].建筑结构学报,2002,23(2):2-12.
[10]欧进萍,吴斌,龙旭.消能减震结构的设计[S]//戴国莹,王亚勇.《建筑抗震设计规范》GB 57011-2001背景材料.北京:中国建筑出版社,2005:323-330.
[11]周云.粘滞阻尼减震结构设计[M].武汉:武汉理工大学出版社,2006.
[12]李宏男,李忠献,祁皑,等.结构振动与控制[M].北京:中国建筑工业出版社,2005.
[13]MARIS N,CONSTANTINOUM,DARGURSHG F.Analytical model of viscoelastic fluid dampers[J].Journal of Structur-al Engineering,ASCE,1993,119(11):3 310-3 325.
[14]MARIS N,CONSTANTINOU M C.Fractional derivative model for viscous damper[J].Journal of Structural Engineering,ASCE,1991,117(9):2 708-2 724.
[15]朱位秋.非线性随机振动理论的近期发展[J].力学进展,1994,24(2):163-172.
[16]ZHUW Q.Recent developments and application of the stochastic averaging method in random Vibration[J].Applied Me-chanics Reviews,1996,49(10):72-80.
[17]ZHU W Q,CAI G Q.Nonlinear Stochastic dynamics:a survey of recent development[J].Acta Mechanics Siuia,2002,18(6):551-566.
[18]ZHU W Q.Nonlinear stochastic dynamics and control in Hamiltonian formulation[J].Applied Mechanics Reviews,2006,59(6):230-248.
[19]朱位秋.随机振动[M].北京:科学出版社,1998.
[20]李创第,邹万杰.非线性流滞阻尼器耗能结构随机地震响应和首超时间分析[J].振动与冲击,2007,26(11):87-90.
[21]李创第,李桂青.非线性时变结构时变动力可靠性分析的包络过程法[J].广西大学学报:自然科学版,1998,23(4):266-269.
[22]李创第,李敦.结构在水平与竖向随机地震同时作用下的相关函数和谱密度[J].工程力学,2008,25(8):156-163.
[23]李创第,邹万杰.结构在水平与竖向地震同时作用的非平稳响应[J].土木工程学报,2005,38(6):25-34.
[24]黄冬梅,李创第,陈俊忠.结构—土相互作用体系的地震作用取值———基于规范地震动模型的复模态时域法[J].振动工程学报,2006,19(4):571-577.
[25]黄冬梅,李创第,朱乐乐.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.
[26]李创第,陈俊忠,黄冬梅.单自由度“加层”减震结构地震作用取值的复模态法[J].应用力学学报,2007,24(1):160-164.
[27]李创第,陈俊忠,黄冬梅.多自由度“加层”减震结构地震作用取值的复模态法[J].哈尔滨工业大学学报,2009,41(4):201-203.
[28]李桂青,曹宏,李秋胜.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.
[29]TSENG C C,PEI S C,HSIAS C.Computation of fractional derivative using Fourier transform and digital FIR differentiator[J].Signal Processing,2000,80:151-159.
[2]SOONG TT,DARGUSHG F.Passive energy dissipation systems in structural engineering[M].England:John Wiley andSons Ltd,1997.
[3]杨仕升,郝效强,秦荣.钢筋混凝土结构薄弱环节与抗震加固分析研究[J].广西大学学报:自然科学版,2008,33(3):211-215.
[4]瞿伟廉.高层建筑和高耸结构的风振控制设计[M].武汉:武汉测绘科技大学出版社,1991.
[5]欧进萍,吴斌,龙旭.耗能减振结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98-107.
[6]李创第,葛新广.带五种被动减振器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,33(4):144-152.
[7]李创第,黄天立.TMD控制优化设计与振动台试验研究[J].土木工程学报,2006,33(7):19-25.
[8]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[9]周锡元,阎淮明,杨润林.建筑结构的隔震、减震和振动控制[J].建筑结构学报,2002,23(2):2-12.
[10]欧进萍,吴斌,龙旭.消能减震结构的设计[S]//戴国莹,王亚勇.《建筑抗震设计规范》GB 57011-2001背景材料.北京:中国建筑出版社,2005:323-330.
[11]周云.粘滞阻尼减震结构设计[M].武汉:武汉理工大学出版社,2006.
[12]李宏男,李忠献,祁皑,等.结构振动与控制[M].北京:中国建筑工业出版社,2005.
[13]MARIS N,CONSTANTINOUM,DARGURSHG F.Analytical model of viscoelastic fluid dampers[J].Journal of Structur-al Engineering,ASCE,1993,119(11):3 310-3 325.
[14]MARIS N,CONSTANTINOU M C.Fractional derivative model for viscous damper[J].Journal of Structural Engineering,ASCE,1991,117(9):2 708-2 724.
[15]朱位秋.非线性随机振动理论的近期发展[J].力学进展,1994,24(2):163-172.
[16]ZHUW Q.Recent developments and application of the stochastic averaging method in random Vibration[J].Applied Me-chanics Reviews,1996,49(10):72-80.
[17]ZHU W Q,CAI G Q.Nonlinear Stochastic dynamics:a survey of recent development[J].Acta Mechanics Siuia,2002,18(6):551-566.
[18]ZHU W Q.Nonlinear stochastic dynamics and control in Hamiltonian formulation[J].Applied Mechanics Reviews,2006,59(6):230-248.
[19]朱位秋.随机振动[M].北京:科学出版社,1998.
[20]李创第,邹万杰.非线性流滞阻尼器耗能结构随机地震响应和首超时间分析[J].振动与冲击,2007,26(11):87-90.
[21]李创第,李桂青.非线性时变结构时变动力可靠性分析的包络过程法[J].广西大学学报:自然科学版,1998,23(4):266-269.
[22]李创第,李敦.结构在水平与竖向随机地震同时作用下的相关函数和谱密度[J].工程力学,2008,25(8):156-163.
[23]李创第,邹万杰.结构在水平与竖向地震同时作用的非平稳响应[J].土木工程学报,2005,38(6):25-34.
[24]黄冬梅,李创第,陈俊忠.结构—土相互作用体系的地震作用取值———基于规范地震动模型的复模态时域法[J].振动工程学报,2006,19(4):571-577.
[25]黄冬梅,李创第,朱乐乐.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.
[26]李创第,陈俊忠,黄冬梅.单自由度“加层”减震结构地震作用取值的复模态法[J].应用力学学报,2007,24(1):160-164.
[27]李创第,陈俊忠,黄冬梅.多自由度“加层”减震结构地震作用取值的复模态法[J].哈尔滨工业大学学报,2009,41(4):201-203.
[28]李桂青,曹宏,李秋胜.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.
[29]TSENG C C,PEI S C,HSIAS C.Computation of fractional derivative using Fourier transform and digital FIR differentiator[J].Signal Processing,2000,80:151-159.
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