电磁调谐质量阻尼器的H_2参数优化及对结构减震分析
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摘要
利用电磁换能器代替传统型调谐质量阻尼器中的黏性阻尼,形成一种具有结构减震与能量收集双重功能的电磁调谐质量阻尼器(electromagnetic tuned mass damper,EMTMD)。通过分析电磁换能器的动力学模型,建立了电磁调谐质量阻尼器的力学模型。将电磁调谐质量阻尼器与单自由度结构相结合,建立耦合结构受地震作用时的动力学模型。基于H2优化理论,即以主结构位移均方根值最小为目标函数,对EMTMD进行参数优化,得到EMTMD的结构频率比、电磁阻尼比和机电耦合系数的参数优化解析解。通过频域和时域两种方法数值仿真分析了EMTMD对结构减震与能量收集的性能。结果表明,在最优状态下,EMTMD对结构位移、加速度峰值和均方根的减振性能略优于经典TMD,且其能量收集的平均功率高达约4.05×105 W。
In this paper,a novel electromagnetic tuned mass damper(EMTMD)is proposed,which can perform the vibration control and energy harvesting simultaneously.The novel feature of the damper consists in that the viscous damping of the traditional tuned mass damper is replaced by the electromagnetic transducer.The mechanical property of the electromagnetic transducer is analyzed,and the dynamical model of the EMTMD is established.To analyze the performance of the EMTMD,the coupled EMTMD and a single degree of freedom structure system under seismic excitation is introduced.Based on the H2 norm with its aim to minimize the root mean square(RMS)value of structure damages,the three closed-form solutions of the parameters,i.e.the mechanical tuning ratio,the electrical damping ratio,the electrical tuning ratio,are obtained.With the optimal parameters,the frequency and time domain numerical simulations of the EMTMD are conducted to analyze the performance of the vibration mitigation and energy harvesting.The results show that in the optimal condition,the reduction of the peak and RMS value of displacement and acceleration of the EMTMD is superior to the classical TMD.Meanwhile,the average power of the energy harvesting is 4.05×105 W.
In this paper,a novel electromagnetic tuned mass damper(EMTMD)is proposed,which can perform the vibration control and energy harvesting simultaneously.The novel feature of the damper consists in that the viscous damping of the traditional tuned mass damper is replaced by the electromagnetic transducer.The mechanical property of the electromagnetic transducer is analyzed,and the dynamical model of the EMTMD is established.To analyze the performance of the EMTMD,the coupled EMTMD and a single degree of freedom structure system under seismic excitation is introduced.Based on the H2 norm with its aim to minimize the root mean square(RMS)value of structure damages,the three closed-form solutions of the parameters,i.e.the mechanical tuning ratio,the electrical damping ratio,the electrical tuning ratio,are obtained.With the optimal parameters,the frequency and time domain numerical simulations of the EMTMD are conducted to analyze the performance of the vibration mitigation and energy harvesting.The results show that in the optimal condition,the reduction of the peak and RMS value of displacement and acceleration of the EMTMD is superior to the classical TMD.Meanwhile,the average power of the energy harvesting is 4.05×105 W.
引文
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[17]Inoue T,Ishida Y,Sumi M.Vibration suppression using electromagnetic resonant shunt damper[J].Journal of Vibration&Acoustics,2008,130(4):2727—2747.
[18]Tang X,Zuo L.Simulation and experiment validation of simultaneous vibration control and energy harvesting from buildings using Tuned Mass Dampers[C].Proceedings of the American Control Conference,San Francisco:CA,2012:3134—3139.
[19]Cui W,Tang X,Zuo L.H2optimization of electricity-generating tuned mass dampers for simultaneous vibration control and energy harvesting[J].Proceeding of SPIE—The International Society for Optical Engineering,2013,8688(3):1—7.
[20]李晓华,王宝基,薛中会.磁耦合调谐质量阻尼器的参数优化及减振效果[J].河南科技大学学报自然科学版,2014(4):86—91.Li Xiaohua,Wang Baoji,Xue Zhonghui.Parameter optimization and vibration control effect of TMD with magnetic coupling[J].Journal of Henan University of Science and Technology:Natural Sciennce,2014,(4):86—91.
[21]陈政清,汪志昊.基于能量回收的土木工程结构振动控制[J].建筑科学与工程学报,2009,26(2):9—14.Chen Zhengqing,Wang Zhihao.Structural vibration Control based on the energy harvesting in civil engineering[J].Journal of Architecture and Civil Engineering,2009,26(2):9—14.
[22]Shen W,Zhu S.Harvesting energy via electromagnetic damper:Application to bridge stay cables[J].Journal of Intelligent Material Systems and Structures,2015,26(1):3—19.
[23]Zuo L,Cui W.Dual-functional energy-harvesting and vibration control:electromagnetic resonant shunt series tuned mass dampers[J].Journal of Vibration and Acoustics,2013,135(5):510181—510189.
[24]Doyle J.Robust and optimal control[J].IEEE Conference on Decision and Control,2002,2(97):1595—1598.
[25]Nishihara O,Asami T.Closed-form solutions to the exact optimizations of dynamic vibration absorbers(minimizations of the maximum amplitude magnification factors)[J].Journal of Vibration&Acoustics,2002,124(4):576—582.
[26]Asami T,Nishihara O,Baz A M.Analytical Solutions to H∞and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J].Journal of Vibration&Acoustics,2002,124(2):284—295.
[2]Soong T T,Jr B F S.Supplemental energy dissipation:state-of-the-art and state-of-the-practice[J].Engineering Structures,2002,24(3):243—259.
[3]茹继平.土木基础设施减灾基础研究进展与趋势[J].土木工程学报,2000,33(6):1—5.Ru Jiping.Development of fundamental researches on disaster mitigation of civil infrastructure systems[J].China Civil Engineering Journal,2000,33(6):1—5.
[4]欧进萍.结构振动控制:主动、半主动和智能控制[M].北京:科学出版社,2003.
[5]Frahm H.Device for Damping Vibrations of Bodies[M].US.1911.
[6]Ormondroyd J,Hartog J P D.The theory of dynamic vibration absorber[J].Journal of Applied Mechanics,1928,49:A9—A22.
[7]Hartog,De J P.Mechanical Vibrations[M].4th ed.McGraw-Hill Book Company,Inc.,1956.
[8]Warburton G B.Optimum absorber parameters for various combinations of response and excitation parameters[J].Earthquake Engineering&Structural Dynamics,1982,10(3):381—401.
[9]Ghosh A,Basu B.A closed-form optimal tuning criterion for TMD in damped structures[J].Structural Control&Health Monitoring,2007,14(4):681—692.
[10]Anh N D,Nguyen N X.Design of TMD for damped linear structures using the dual criterion of equivalent linearization method[J].International Journal of Mechanical Sciences,2013,77(77):164—170.
[11]李春祥,熊学玉,程斌.基于参数组合和加速度传递函数的最优MTMD研究[J].振动与冲击,2001,20(3):50—54.Li Chunxiang,Xiong Xueyu,Cheng Bin.Research on the optimum MTMD based on parameter combinations and acceleration transfer function[J].Journal of Vibration and Shock,2001,20(3):50—54.
[12]王磊,谭平,赵卿卿.随机结构-TMD优化设计与概率密度演化研究[J].振动工程学报,2015,28(2):285—290.Wang Lei,Tan Ping,Zhao Qingqing.Optimal design and probability density evolution analysis of tuned mass damper for stochastic structures[J].Journal of Vibration Eingineering,2015,28(2):285—290.
[13]Nerves A C,Krishnan R.A strategy for active control of tall civil structures using regenerative electric actuators[C].Proceedings of 11th ASCE Engineering Mechanics Specialists Conference,Florida,1996,503-506.
[14]孙作玉,刘季.结构振动的无能源主动控制[J].地震工程与工程振动,1999,19(3):102—105.Sun Zuoyu,Liu Ji.Active structural vibration conrol without power supply[J],Earthquake Engineering and Eingineering Vibration,1999,19(3):102—105.
[15]张永山,孙作玉,何玉敖.换能器与作动器同层布置时的无能源主动控制[J].哈尔滨工业大学学报,2001,33(3):333—335.Zhang Yingshan,Sun Zuoyu,He Yuao.ACWPS with transducer and actuator placed on the same floor[J].Journal of Harbin Institute of Technology,2001,33(3):333—335.
[16]Behrens S,Fleming A J,Moheimani S O R.Vibration isolation using a shunted electromagnetic transducer[C].Proc.Spie,Smart Structure and Materials,2004,5386:506—515.
[17]Inoue T,Ishida Y,Sumi M.Vibration suppression using electromagnetic resonant shunt damper[J].Journal of Vibration&Acoustics,2008,130(4):2727—2747.
[18]Tang X,Zuo L.Simulation and experiment validation of simultaneous vibration control and energy harvesting from buildings using Tuned Mass Dampers[C].Proceedings of the American Control Conference,San Francisco:CA,2012:3134—3139.
[19]Cui W,Tang X,Zuo L.H2optimization of electricity-generating tuned mass dampers for simultaneous vibration control and energy harvesting[J].Proceeding of SPIE—The International Society for Optical Engineering,2013,8688(3):1—7.
[20]李晓华,王宝基,薛中会.磁耦合调谐质量阻尼器的参数优化及减振效果[J].河南科技大学学报自然科学版,2014(4):86—91.Li Xiaohua,Wang Baoji,Xue Zhonghui.Parameter optimization and vibration control effect of TMD with magnetic coupling[J].Journal of Henan University of Science and Technology:Natural Sciennce,2014,(4):86—91.
[21]陈政清,汪志昊.基于能量回收的土木工程结构振动控制[J].建筑科学与工程学报,2009,26(2):9—14.Chen Zhengqing,Wang Zhihao.Structural vibration Control based on the energy harvesting in civil engineering[J].Journal of Architecture and Civil Engineering,2009,26(2):9—14.
[22]Shen W,Zhu S.Harvesting energy via electromagnetic damper:Application to bridge stay cables[J].Journal of Intelligent Material Systems and Structures,2015,26(1):3—19.
[23]Zuo L,Cui W.Dual-functional energy-harvesting and vibration control:electromagnetic resonant shunt series tuned mass dampers[J].Journal of Vibration and Acoustics,2013,135(5):510181—510189.
[24]Doyle J.Robust and optimal control[J].IEEE Conference on Decision and Control,2002,2(97):1595—1598.
[25]Nishihara O,Asami T.Closed-form solutions to the exact optimizations of dynamic vibration absorbers(minimizations of the maximum amplitude magnification factors)[J].Journal of Vibration&Acoustics,2002,124(4):576—582.
[26]Asami T,Nishihara O,Baz A M.Analytical Solutions to H∞and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J].Journal of Vibration&Acoustics,2002,124(2):284—295.