单自由度混联Ⅱ型惯容减震体系的随机地震响应与参数设计
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摘要
为了解混联Ⅱ型惯容减震系统(SPIS-Ⅱ)的减震机理,该文对设置SPIS-Ⅱ的单自由度体系进行了随机地震响应变化规律的研究并提出了参数优化设计的方法。首先在体系运动微分方程的基础上,基于随机振动的理论和方法推导了SPIS-Ⅱ单自由度体系在地震作用下频域响应传递函数及随机响应均方根的表达式。接着以金井清谱为随机地震输入模型,基于随机响应表达式研究了地震动参数和SPIS-Ⅱ关键参数对单自由度体系响应变化规律的影响。然后在参数研究的基础上,提出了SPIS-Ⅱ单自由度体系在地震作用下的实用优化设计方法,该方法以性能需求为设计目标,可同时考虑响应与成本的控制以及输入地震动的频谱特征。最后根据所提出方法编制程序进行了一系列实例设计,并进行了动力时程分析验证,设计及分析的结果均证实了该文提出方法的有效性。
In order to comprehend the response mitigation mechanism of a specified inerter system named series-parallel-Ⅱ inerter system(SPIS-Ⅱ),the response variation trends for a single-degree-of-freedom(SDOF) system with SPIS-Ⅱ are studied and the parametric optimal design method is proposed.The mathematical expressions of frequency-domain response transfer functions and root-mean-square random responses of a SDOF system with SPIS-Ⅱ are derived based on the equations of motion and theories in random vibration.Then the response variation trends of a SDOF system with SPIS-Ⅱ are investigated by adopting Kanai-Tajimi's spectrum as a seismic input model along with the change of key parameters of seismic ground motion and SPIS-Ⅱ.Based on parametric studies,a practical optimal design method of a SDOF system with SPIS-Ⅱ is proposed.For this method,seismic performance demand is taken as the design target and response control,cost minimization,and spectral properties of seismic excitations are all considered during design.Finally,a computer program is developed according to the proposed method to conduct design examples,and dynamic time-history analyses arealso carried out.The results of example design and analysis prove the effectiveness of the proposed design method.
In order to comprehend the response mitigation mechanism of a specified inerter system named series-parallel-Ⅱ inerter system(SPIS-Ⅱ),the response variation trends for a single-degree-of-freedom(SDOF) system with SPIS-Ⅱ are studied and the parametric optimal design method is proposed.The mathematical expressions of frequency-domain response transfer functions and root-mean-square random responses of a SDOF system with SPIS-Ⅱ are derived based on the equations of motion and theories in random vibration.Then the response variation trends of a SDOF system with SPIS-Ⅱ are investigated by adopting Kanai-Tajimi's spectrum as a seismic input model along with the change of key parameters of seismic ground motion and SPIS-Ⅱ.Based on parametric studies,a practical optimal design method of a SDOF system with SPIS-Ⅱ is proposed.For this method,seismic performance demand is taken as the design target and response control,cost minimization,and spectral properties of seismic excitations are all considered during design.Finally,a computer program is developed according to the proposed method to conduct design examples,and dynamic time-history analyses arealso carried out.The results of example design and analysis prove the effectiveness of the proposed design method.
引文
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[2]Saaed T E,Nikolakopoulos G,Jonasson J E,et al.Astate-of-the-art review of structural control systems[J].Journal of Vibration and Control,2015,21(5):919-937.
[3]杨青顺,甄伟,陆新征,等.带端部阻尼器伸臂桁架的抗震性能试验研究[J].工程力学,2018,35(2):47-58.Yang Qingshun,Zhen Wei,Lu Xinzheng,et al.Experimental study on the seismic performance of damped outriggers[J].Engineering Mechanics,2018,35(2):47-58.(in Chinese)
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[5]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)
[6]Arakaki T,Kuroda H,Arima F,et al.Development of seismic devices applied to ball screw:Part 1 Basic performance test of RD-series[J].AIJ Journal of Technology and Design,1999,5(8):239-244.
[7]Smith M C.Synthesis of mechanical networks:The inerter[J].IEEE Transactions on Automatic Control,2002,47(10):1648-1662.
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[9]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)
[10]杨晓峰,沈钰杰,陈龙,等.基于动力吸振理论的车辆ISD悬架设计与性能分析[J].汽车工程,2014,36(10):1262-1266.Yang Xiaofeng,Shen Yujie,Chenlong,et al.Design and performance analysis of vehicle ISD suspension based on dynamic vibration absorber theory[J].Automotive Engineering,2014,36(10):1262-1266.(in Chinese)
[11]毛明,王乐,陈轶杰,等.惯容器及惯容器-弹簧-阻尼器悬架研究进展[J].兵工学报,2016,37(3):525-534.Mao Ming,Wang Le,Chen Yijie,et al.Research progress in inerter and inerter-spring-damper suspension[J].Acta Armamentarii,2016,37(3):525-534.(in Chinese)
[12]Saito K,Kurita S,Inoue N.Optimum response control of1-DOF system using linear viscous damper with inertial mass and its Kelvin-type modeling[J].Journal of Structural Engineering,2007,53:53-66.
[13]Ikago K,Saito K,Inoue N.Seismic control of single-degree-of-freedom structure using tuned viscous mass damper[J].Earthquake Engineering&Structural Dynamics,2012,41(3):453-474.
[14]Pan C,Zhang R F,Luo H,et al.Demand-based optimal design of oscillator with parallel-layout viscous inerter damper[J].Structural Control and Health Monitoring,2018,25(1):e2051.
[15]Kida H,Watanabe Y,Nakaminami S,et al.Full-scale dynamic tests of tuned viscous mass damper with force restriction mechanism and Its analytical verification[J].Journal of Structural and Construction Engineering Architectural Institute of Japan,2011,76(665):1271-1280.
[16]Nakamura Y,Fukukita A,Tamura K,et al.Seismic response control using electromagnetic inertial mass dampers[J].Earthquake Engineering and Structural Dynamics,2014,43(4):507-527.
[17]Lazar I F,Neild S A,Wagg D J.Using an inerter-based device for structural vibration suppression[J].Earthquake Engineering&Structural Dynamics,2014,43(8):1129-1147.
[18]罗浩,张瑞甫,翁大根,等.一种旋转黏滞质量阻尼器对结构响应的控制研究[J].防灾减灾工程学报,2016,36(2):295-301.Luo Hao,Zhang Ruifu,Weng Dagen,et al.Study of a series viscous mass damper in the control of structural response[J].Journal of Disaster Prevention and Mitigation Engineering,2016,36(2):295-301.(in Chinese)
[19]Luo H,Zhang R F,Weng D G.Mitigation of liquid sloshing in storage tanks by using a hybrid control method[J].Soil Dynamics and Earthquake Engineering,2016,90:183-195.
[20]阎武通,韩冰,文永奎.新型调谐黏滞质量阻尼器对斜拉桥的减震控制分析[J].土木工程学报,2016,49(S1):66-71.Yan Wutong,Han Bing,Wen Yongkui,et al.Seismic control analysis of cable-stayed bridge based on tuned viscous mass damper[J].China Civil Engineering Journal,2016,49(S1):66-71.(in Chinese)
[21]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,2017,143(4):4016201-4016207.
[22]Kanai K.Semi-empirical formula for the seismic characteristics of the ground[J].Bulletin of Earthquake Research Institute,University of Tokyo,1957,35(2):309-325.
[23]Papageorgiou C,Houghton N E,Smith M C.Experimental testing and analysis of inerter devices[J].Journal of Dynamic Systems,Measurement and Control,Transactions of the ASME,2009,131(1):1-11.
[24]Swift S J,Smith M C,Glover A R,et al.Design and modelling of a fluid inerter[J].International Journal of Control,2013,86(11):2035-2051.
[25]Hu Y,Chen M Z Q,Shu Z,et al.Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution[J].Journal of Sound and Vibration,2015,346:17-36.
[26]Crandall S H,Mark W D.Random vibration in mechanical systems[M].New York:Academic Press,2014.
[27]Chankong V,Haimes Y.Multiobjective decision making theory and methodology[M].New York:Elsevier,1983.
[28]Oliphant T E.Python for scientific computing[J].Computing in Science&Engineering,2007,9(3):10-20.
[2]Saaed T E,Nikolakopoulos G,Jonasson J E,et al.Astate-of-the-art review of structural control systems[J].Journal of Vibration and Control,2015,21(5):919-937.
[3]杨青顺,甄伟,陆新征,等.带端部阻尼器伸臂桁架的抗震性能试验研究[J].工程力学,2018,35(2):47-58.Yang Qingshun,Zhen Wei,Lu Xinzheng,et al.Experimental study on the seismic performance of damped outriggers[J].Engineering Mechanics,2018,35(2):47-58.(in Chinese)
[4]Den Hartog J P.Mechanical Vibrations[M].:New York:McGraw-Hill Book Company,1956.
[5]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)
[6]Arakaki T,Kuroda H,Arima F,et al.Development of seismic devices applied to ball screw:Part 1 Basic performance test of RD-series[J].AIJ Journal of Technology and Design,1999,5(8):239-244.
[7]Smith M C.Synthesis of mechanical networks:The inerter[J].IEEE Transactions on Automatic Control,2002,47(10):1648-1662.
[8]Smith M C,Wang F U C.Performance benefits in passive vehicle suspensions employing inerters[J].Vehicle System Dynamics,2004,42(4):235-257.
[9]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)
[10]杨晓峰,沈钰杰,陈龙,等.基于动力吸振理论的车辆ISD悬架设计与性能分析[J].汽车工程,2014,36(10):1262-1266.Yang Xiaofeng,Shen Yujie,Chenlong,et al.Design and performance analysis of vehicle ISD suspension based on dynamic vibration absorber theory[J].Automotive Engineering,2014,36(10):1262-1266.(in Chinese)
[11]毛明,王乐,陈轶杰,等.惯容器及惯容器-弹簧-阻尼器悬架研究进展[J].兵工学报,2016,37(3):525-534.Mao Ming,Wang Le,Chen Yijie,et al.Research progress in inerter and inerter-spring-damper suspension[J].Acta Armamentarii,2016,37(3):525-534.(in Chinese)
[12]Saito K,Kurita S,Inoue N.Optimum response control of1-DOF system using linear viscous damper with inertial mass and its Kelvin-type modeling[J].Journal of Structural Engineering,2007,53:53-66.
[13]Ikago K,Saito K,Inoue N.Seismic control of single-degree-of-freedom structure using tuned viscous mass damper[J].Earthquake Engineering&Structural Dynamics,2012,41(3):453-474.
[14]Pan C,Zhang R F,Luo H,et al.Demand-based optimal design of oscillator with parallel-layout viscous inerter damper[J].Structural Control and Health Monitoring,2018,25(1):e2051.
[15]Kida H,Watanabe Y,Nakaminami S,et al.Full-scale dynamic tests of tuned viscous mass damper with force restriction mechanism and Its analytical verification[J].Journal of Structural and Construction Engineering Architectural Institute of Japan,2011,76(665):1271-1280.
[16]Nakamura Y,Fukukita A,Tamura K,et al.Seismic response control using electromagnetic inertial mass dampers[J].Earthquake Engineering and Structural Dynamics,2014,43(4):507-527.
[17]Lazar I F,Neild S A,Wagg D J.Using an inerter-based device for structural vibration suppression[J].Earthquake Engineering&Structural Dynamics,2014,43(8):1129-1147.
[18]罗浩,张瑞甫,翁大根,等.一种旋转黏滞质量阻尼器对结构响应的控制研究[J].防灾减灾工程学报,2016,36(2):295-301.Luo Hao,Zhang Ruifu,Weng Dagen,et al.Study of a series viscous mass damper in the control of structural response[J].Journal of Disaster Prevention and Mitigation Engineering,2016,36(2):295-301.(in Chinese)
[19]Luo H,Zhang R F,Weng D G.Mitigation of liquid sloshing in storage tanks by using a hybrid control method[J].Soil Dynamics and Earthquake Engineering,2016,90:183-195.
[20]阎武通,韩冰,文永奎.新型调谐黏滞质量阻尼器对斜拉桥的减震控制分析[J].土木工程学报,2016,49(S1):66-71.Yan Wutong,Han Bing,Wen Yongkui,et al.Seismic control analysis of cable-stayed bridge based on tuned viscous mass damper[J].China Civil Engineering Journal,2016,49(S1):66-71.(in Chinese)
[21]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,2017,143(4):4016201-4016207.
[22]Kanai K.Semi-empirical formula for the seismic characteristics of the ground[J].Bulletin of Earthquake Research Institute,University of Tokyo,1957,35(2):309-325.
[23]Papageorgiou C,Houghton N E,Smith M C.Experimental testing and analysis of inerter devices[J].Journal of Dynamic Systems,Measurement and Control,Transactions of the ASME,2009,131(1):1-11.
[24]Swift S J,Smith M C,Glover A R,et al.Design and modelling of a fluid inerter[J].International Journal of Control,2013,86(11):2035-2051.
[25]Hu Y,Chen M Z Q,Shu Z,et al.Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution[J].Journal of Sound and Vibration,2015,346:17-36.
[26]Crandall S H,Mark W D.Random vibration in mechanical systems[M].New York:Academic Press,2014.
[27]Chankong V,Haimes Y.Multiobjective decision making theory and methodology[M].New York:Elsevier,1983.
[28]Oliphant T E.Python for scientific computing[J].Computing in Science&Engineering,2007,9(3):10-20.
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