SDOF-TMD控制系统能量响应特性与能量谱研究
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摘要
目的研究弹性单自由度(SDOF)结构调谐质量阻尼(TMD)控制系统的能量响应特性和控制系统的能量谱变化规律.方法采用地震激励下结构位移均方值最小为优化目标的TMD最优参数表达式,基于相对能量计算公式,并考虑了TMD子结构的不同频率比、质量比和阻尼比等参数摄动来分析控制系统能量谱变化规律.结果在El centro地震作用下,TMD能较好地控制主结构的各项能量响应.TMD控制系统在短周期0~0.5 s和长周期3.2~4 s范围内,系统能量对TMD参数变化不敏感;在1.0~3.2 s范围内,质量比越大,其动能、势能和输入能的控制效果越好,且存在最优调谐频率比;控制系统的能量反应对TMD子结构的阻尼比变化不敏感.结论TMD需要积累较大的能量才能对结构有较好的控制效果,TMD子结构参数是影响TMD控制系统能量谱变化规律的重要指标.
The purpose of this paper is to research the rules of control system energy response and energy spectrum for the single degree of freedom(SDOF) structure with TMD control.According to the optimal formula for TMD system with minimizing the structural displacement STD and based on the relative energy calculation formula,the process of TMD-control system energy recurs and the three factors are considered to influence the control system energy response varying,including the different frequency ratio,mass ratio and damping ratio of the TMD.The result shows that under the El centro seismic action the main energy can be controlled better with TMD and the parameters of TMD are the important indexes to affect the TMD-control system energy response.There are consistent relationship between the main structure displacement and system energy control.During the short period of 0~0.5 s and the long period 3.2~4 s,the control system energy is not sensitive to the TMD′s parameters varying;During the 1.0~3.2 s periods,the larger the mass ratio,the better the control effect of the energy spectrum is,that exists the optimizing tuned frequency ratio,and the system energy difference is not obvious with the usual TMD′s damping ratio range.
The purpose of this paper is to research the rules of control system energy response and energy spectrum for the single degree of freedom(SDOF) structure with TMD control.According to the optimal formula for TMD system with minimizing the structural displacement STD and based on the relative energy calculation formula,the process of TMD-control system energy recurs and the three factors are considered to influence the control system energy response varying,including the different frequency ratio,mass ratio and damping ratio of the TMD.The result shows that under the El centro seismic action the main energy can be controlled better with TMD and the parameters of TMD are the important indexes to affect the TMD-control system energy response.There are consistent relationship between the main structure displacement and system energy control.During the short period of 0~0.5 s and the long period 3.2~4 s,the control system energy is not sensitive to the TMD′s parameters varying;During the 1.0~3.2 s periods,the larger the mass ratio,the better the control effect of the energy spectrum is,that exists the optimizing tuned frequency ratio,and the system energy difference is not obvious with the usual TMD′s damping ratio range.
引文
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[3]Abe M,Fujino Y.Dynamic characterization of multi-ple tuned mass dampers and some design formulas[J].Earthquake Engineering and Structural Dynam-ics,1994,23:813-835.
[4]Chen G,Wu J N.Optimal placement of multiple tunemass dampers for seismic structures[J].Journal ofStructural Engineering ASCE,2001,127:1054-1062.
[5]Li C,Liu Y.Further characteristics for multiple tunedmass dampers[J].Journal of Structural EngineeringASCE,2002,128:1362-1365.
[6]Kareem A,Kline S.Performance of multiple massdampers under random loading[J].Journal of Struc-tural Engineering.ASCE,1995,121:348-361.
[7]Wong K K F,Chee Y L.Energy dissipation of tunedmass dampers during earthquake excitations[J].TheStructural Design of Tall and Special Buildings,2004,13:105-121.
[8]周福霖.工程结构减振控制[M].北京:地震出版社,1997.
[9]余钱华,胡世德,范立础.桥梁结构MTMD被动控制机理及试验[J].中国公路学报,2008,21(4):50-55.
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