电磁调谐双质阻尼器的H_2参数优化及对结构减震分析
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摘要
该文在利用电磁阻尼单元代替经典型调谐质量阻尼器中的粘性阻尼单元的基础上,引入惯质单元,形成一种新型的具有结构减振和能量收集双重功能的电磁调谐双质阻尼器(electromagnetic tuned mass-inerter damper,EM-TMID)。依据达朗伯定理,建立EM-TMID与单自由度结构耦合结构受地震作用时的动力学模型。然后基于H2优化理论,即以主结构位移均方根值最小为目标函数,对EM-TMID进行参数优化,得到EM-TMID的结构频率比、电磁阻尼比和机电耦合系数的最优解析式。最后通过频域和时域两种仿真方法数值仿真分析了EM-TMID对结构的减震和能量收集的双重性能。结果表明,在频域分析中,EM-TMID的主结构位移峰值和频响面积均优于经典TMD、EM-TMD和TMDI。在时域分析中,EM-TMID对结构位移、加速度的峰值和均方根值的减震性能均优于经典TMD,同时能够进行能量收集。
A novel electromagnetic shunt tuned mass-inerter damper(EM-TMID) is proposed, which can realize dual functions of both vibration suppression and energy harvesting. A novel feature of the damper is that the viscous damping of traditional tuned mass dampers is replaced by that of electromagnetic transducers with inertance. According to the Alembert's theorem, the dynamic model of a coupled EM-TMID and a single degree of freedom structural system under seismic excitation is established. Based on the H2 norm method with the aim of minimizing the root mean square value of the damage to the main structure, solutions of the three parameters,that is, the mechanical tuning ratio, electrical damping ratio and electromagnetic mechanical coupling coefficient,are obtained. With the optimal parameters, the frequency-domain and time-domain numerical simulations of the EM-TMID are conducted to analyze the dual functions of the vibration suppression and energy harvesting. The results show that in the frequency domain, the EM-TMID is superior to the classical TMD, EM-TMD and TMDI in terms of the reduction of the peak and area of the frequency response of the displacement of the main structure.In the time domain, the EM-TMID is superior to classical TMDs in terms of the reduction of the peak and root mean square value of displacement and acceleration. Meanwhile, the EM-TMID can also harvest energy.
A novel electromagnetic shunt tuned mass-inerter damper(EM-TMID) is proposed, which can realize dual functions of both vibration suppression and energy harvesting. A novel feature of the damper is that the viscous damping of traditional tuned mass dampers is replaced by that of electromagnetic transducers with inertance. According to the Alembert's theorem, the dynamic model of a coupled EM-TMID and a single degree of freedom structural system under seismic excitation is established. Based on the H2 norm method with the aim of minimizing the root mean square value of the damage to the main structure, solutions of the three parameters,that is, the mechanical tuning ratio, electrical damping ratio and electromagnetic mechanical coupling coefficient,are obtained. With the optimal parameters, the frequency-domain and time-domain numerical simulations of the EM-TMID are conducted to analyze the dual functions of the vibration suppression and energy harvesting. The results show that in the frequency domain, the EM-TMID is superior to the classical TMD, EM-TMD and TMDI in terms of the reduction of the peak and area of the frequency response of the displacement of the main structure.In the time domain, the EM-TMID is superior to classical TMDs in terms of the reduction of the peak and root mean square value of displacement and acceleration. Meanwhile, the EM-TMID can also harvest energy.
引文
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[18]Inoue T,Ishida Y,Sumi M.Vibration suppression using electromagnetic resonant shunt damper[J].Journal of Vibration&Acoustics,2008,130(4):2727―2747.
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[20]Liu Y,Lin C-C,Parker J,et al.Exact H2 optimal tuning and experimental verification of energy-harvesting series electromagnetic tuned-mass dampers[J].Journal of Vibration and Acoustics,2016,138(6):061003.
[21]罗一帆,孙洪鑫,王修勇.电磁调谐质量阻尼器的H2参数优化及对结构减震分析[J].振动工程学报,2018,31(3):529―538.Luo Yifan,Sun Hongxin,Wang Xiuyong.H2 paramenters optimization and vibration reduction analysis of electromagnetic tuned mass damper[J].Journal of Vibration Engineering,2018,31(3):529―538.(in Chinese)
[22]Zuo L,Tang X.Large-scale vibration energy harvesting[J].Journal of Intelligent Material Systems and Structures,2013,24(11):1405―1430.
[23]Shen W,Zhu S,Zhu H.Experimental study on using electromagnetic devices on bridge stay cables for simultaneous energy harvesting and vibration damping[J].Smart Material and Structures,2016,25(6):065011.
[24]Doyle J.Robust and optimal control[C].Proceedings of the IEEE Conference on the 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]Rana R,Soong T T.Parametric study and simplified design of tuned mass dampers[J].Engineering Structures,1998,20(3):193―204.
[3]林均岐,王云剑.调谐质量阻尼器的优化分析[J].地震工程与工程振动,1996,16(1):116―121.Lin Junqi,Wang Yunjian.Optimal analysis of tuned mass damper[J].Earthquake Engineering and Engineering vibration,1996,16(1):116―121.(in Chinese)
[4]李宏男,王苏岩.利用TMD减小高层建筑地震反应的研究[J].工程力学,1997,(a03):136―140.Li Hongnan,Wang Suyan.Reducing the seismic response of high-rise buildings with TMD[J].Engineering Mechanics,1997,(a03):136―140.(in Chinese)
[5]李春祥.土木工程结构的双层多重调谐质量阻尼器控制策略[J].地震工程与工程振动,2005,25(1):113―119.Li Chunxiang.Dual layer multiple tuned mass damper control strategy of civil engineering structures[J].Earthquake engineering and engineering vibration,2005,25(1):113―119.(in Chinese)
[6]王文熙.桥梁TMD系统的参数优化与设计[D].湖南大学,2014.Wang Wenxi.Parametric optimization and design of bridge TMD system[D].Hu’nan:Hunan University,2014.(in Chinese)
[7]喻梅,廖海黎,李明水,等.基于经验线性涡激力的桥梁涡激振动TMD控制[J].工程力学,2013,30(6):269―274.Yu Mei,Liao Haili,Li Mingshui,et al.Suppression of vortex-induced vibration of bridges using TMD based on linear empirical vortex-shedding forces model[J].Engineering Mechanics,2013,30(6):269―274.(in Chinese)
[8]刘良坤,谭平,闫维明,等.一种NES与TMD的混合控制方案研究[J].工程力学,2017,34(9):64―72.Liu Liangkun,Tan Ping,Yan Weiming,et al.Analysis of a hybrid scheme comprised of nonlinear energy sink and tuned mass damper[J].Engineering Mechanics,2017,34(9):64―72.(in Chinese)
[9]Smith M C.Synthesis of mechanical networks:The inerter[J].Automatic Control,IEEE Transactions on,2002,47(10):1648―1662.
[10]孙洪鑫,罗一帆,王修勇,等.电磁调谐双质阻尼器的参数优化及对结构减震分析[J].沈阳建筑大学学报(自然科学版),2018,34(3):410―418.Sun Hongxin,Luo Yifan,Wang Xiuyong,et al.Parametric optimization and vibration control of electromagnetic tuned mass-inerter dampers for the structures[J].Journal of Shenyang Jianzhu University(Natural Science),2018,34(3):410―418.(in Chinese)
[11]陈龙,张孝良,聂佳梅,等.基于半车模型的两级串联型ISD悬架性能分析[J].机械工程学报,2012,48(6):102―108.Chen Long,Zhang Xiaoliang,Nie Jiamei,et al.Performance analysis of two-stage series-connected inerter-spring-damper suspension based on half-car model[J].Journal of Mechanical Engineering,2012,48(6):102―108.(in Chinese)
[12]陈龙,杨晓峰,汪若尘,等.基于二元件ISD结构隔振机理的车辆被动悬架设计与性能研究[J].振动与冲击,2013,32(6):90―95.Chen Long,Yang Xiaofeng,Wang Ruochen,et al.Design and performance study of vehicle passive suspension based on two-element inerter-spring-damper structure vibration isolation mechanism[J].Journal of Shock and Vibration,2013,32(6):90―95.(in Chinese)
[13]Marian L,Giaralis A.Optimal design of a novel tuned mass-damper-inerter(TMDI)passive vibration control configuration for stochastically support-excited structural systems[J].Probabilistic Engineering Mechanics,2014,38:156―164.
[14]Salvi J,Giaralis A.Concept study of a novel energy harvesting-enabled tuned mass-damper-inerter(EH-TMDI)device for vibration control of harmonicallyexcited structures[C].Journal of Physics:Conference Series,2016,744(1):012082.
[15]Nakamura Y,Fukukita A,Tamura K,et al.Seismic response control using electromagnetic inertial mass dampers[J].Earthquake Engineering&Structural Dynamics,2014,43(4):507―527.
[16]Wen Y,Chen Z,Hua X.Design and evaluation of tuned inerter-based dampers for the seismic control of MDOFstructures[J].Journal of Structural Engineering,2016,143(4):04016207.
[17]汪志昊,许艳伟,赵顺波,等.基于表观质量负刚度效应的调谐质量阻尼器频率调节[J].科学技术与工程,2016,16(27):246―250.Wang Zhihao,Xu Yanwei,Zhao Shunbo,et al.Frequency tuning of tuned mass dampers based on negative stiffness generated by apparent mass[J].Science Technology and Engineering,2016,16(27):246―250.(in Chinese)
[18]Inoue T,Ishida Y,Sumi M.Vibration suppression using electromagnetic resonant shunt damper[J].Journal of Vibration&Acoustics,2008,130(4):2727―2747.
[19]Zuo L,Cui W.Dual-functional energy-harvesting and vibration control:electromagnetic resonant shunt series tuned mass dampers[J].Journal of Vibration&Acoustics,2013,135(5):510181―510189.
[20]Liu Y,Lin C-C,Parker J,et al.Exact H2 optimal tuning and experimental verification of energy-harvesting series electromagnetic tuned-mass dampers[J].Journal of Vibration and Acoustics,2016,138(6):061003.
[21]罗一帆,孙洪鑫,王修勇.电磁调谐质量阻尼器的H2参数优化及对结构减震分析[J].振动工程学报,2018,31(3):529―538.Luo Yifan,Sun Hongxin,Wang Xiuyong.H2 paramenters optimization and vibration reduction analysis of electromagnetic tuned mass damper[J].Journal of Vibration Engineering,2018,31(3):529―538.(in Chinese)
[22]Zuo L,Tang X.Large-scale vibration energy harvesting[J].Journal of Intelligent Material Systems and Structures,2013,24(11):1405―1430.
[23]Shen W,Zhu S,Zhu H.Experimental study on using electromagnetic devices on bridge stay cables for simultaneous energy harvesting and vibration damping[J].Smart Material and Structures,2016,25(6):065011.
[24]Doyle J.Robust and optimal control[C].Proceedings of the IEEE Conference on the 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.