摄动结构中基于H_∞范数的调液阻尼器减震优化设计
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摘要
为了减小建筑结构在地震作用下的振动,对调液柱型阻尼器的质量比、频率比和阻尼比进行优化设计.以5层框架建筑结构为例,考虑结构参数的摄动,将优化目标设为地震动到结构动力响应传递函数的H∞范数,得到调液柱型阻尼器最优质量比、频率比和阻尼比的数值分别为0.022 801、0.909 070和0.098 655.采用此最优值,对控制体系的鲁棒性进行验证.结果表明:在频域和时域内,控制系统在地震动作用下对结构参数摄动均具有良好的鲁棒性;当系统的质量、阻尼和刚度的最大摄动量分别达到30%时,系统仍能保持7%以上的减震水平.
In order to reduce the vibration of building structures excited by earthquakes,the mass ratio,frequency ratio,and damping ratio of a tuned liquid column damper( TLCD) are optimized. A five-story reinforced concrete structure building is selected for the numerical example with the consideration of parameter perturbation. The optimization objective is set to be the H∞norm of the transfer function from the ground motion to the structural responses. The acquired optimal mass ratio,frequency ratio,and damping ratio of TLCD are 0. 022 801,0. 909 070,and 0. 098 655,respectively.With these optimal values,the robustness of the control system is verified. The results show that the control system has good robustness for structural parameter perturbation under seismic action in both frequency and time domain. The seismic reduction ratio is still kept above 7% even if the maximum system perturbation of mass,damping,and stiffness reach 30%.
In order to reduce the vibration of building structures excited by earthquakes,the mass ratio,frequency ratio,and damping ratio of a tuned liquid column damper( TLCD) are optimized. A five-story reinforced concrete structure building is selected for the numerical example with the consideration of parameter perturbation. The optimization objective is set to be the H∞norm of the transfer function from the ground motion to the structural responses. The acquired optimal mass ratio,frequency ratio,and damping ratio of TLCD are 0. 022 801,0. 909 070,and 0. 098 655,respectively.With these optimal values,the robustness of the control system is verified. The results show that the control system has good robustness for structural parameter perturbation under seismic action in both frequency and time domain. The seismic reduction ratio is still kept above 7% even if the maximum system perturbation of mass,damping,and stiffness reach 30%.
引文
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[8]陈彦秋,宋鹏云,张继业,等.车辆能量回馈式主动悬架综合控制[J].西南交通大学学报,2012,47(6):974-981.CHEN Yanqiu,SONG Pengyun,ZHANG Jiye,et al.μ-synthesis control for self-powered active suspension of vehicles[J].Journal of Southwest Jiaotong University,2012,47(6):974-981.
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[10]沈文赫,霍林生,李宏男.基于H∞范数的调液阻尼器减震优化设计[J].工程力学,2011,28(11):202-209.SHEN Wenhe,HUO Linsheng,LI Hongnan.H∞norm based optimal design of structural vibration control using liquid dampers[J].Engineering Mechanics,2011,28(11):202-209.
[11]徐赵东,郭迎庆.MATLAB语言在建筑抗震工程中的应用[M].北京:科学出版社,2004:192-198.
[2]JABBARI F,SCHMITENDORF W,YANG J.H∞control for seismic-excited buildings with acceleration feedback[J].Journal of Engineering Mechanics,1995,121(9):994-1002.
[3]DU H P,ZHANG N,NGUYEN H.Mixed H2/H∞control of tall buildings with reduced-order modeling technique[J].Structural Control and Health Monitoring,2008,15(1):64-89.
[4]KOSE I E,SCHMITENDORF W E,JABBARI F,et al.H∞active seismic response control using static output feedback[J].Journal of Engineering Mechanics,1996,122(7):651-659.
[5]CHASE J G,SMITH H A.Robust H∞control considering actuator saturation,part 1:theory[J].Journal of Engineering Mechanics,1996,122(10):976-983.
[6]WANG S G,ROSCHKE P N,YEH H Y.Robust control for structural system with unstructured uncertainties[J].Journal of Engineering Mechanics,2004,130(3):337-346.
[7]张微敬,欧进萍.基于状态反馈的结构鲁棒控制[J].世界地震工程,2002,18(3):37-41.ZHANG Weijing,OU Jinping.Robust control approach of structural vibration based on state feedback[J].World Earthquake Engineering,2002,18(3):37-41.
[8]陈彦秋,宋鹏云,张继业,等.车辆能量回馈式主动悬架综合控制[J].西南交通大学学报,2012,47(6):974-981.CHEN Yanqiu,SONG Pengyun,ZHANG Jiye,et al.μ-synthesis control for self-powered active suspension of vehicles[J].Journal of Southwest Jiaotong University,2012,47(6):974-981.
[9]杨和利.高效馈能半主动悬架设计与性能分析[J].西南交通大学学报,2012,47(5):974-981.YANG Heli.Design and performance analysis of efficient semi-active energy-regenerative suspension[J].Journal of Southwest Jiaotong University,2012,47(5):855-860.
[10]沈文赫,霍林生,李宏男.基于H∞范数的调液阻尼器减震优化设计[J].工程力学,2011,28(11):202-209.SHEN Wenhe,HUO Linsheng,LI Hongnan.H∞norm based optimal design of structural vibration control using liquid dampers[J].Engineering Mechanics,2011,28(11):202-209.
[11]徐赵东,郭迎庆.MATLAB语言在建筑抗震工程中的应用[M].北京:科学出版社,2004:192-198.
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