考虑摩擦效应的颗粒阻尼器力学模型研究及参数分析
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摘要
颗粒阻尼具有高度非线性特性且影响因素复杂,在土木工程减振控制的研究和应用处于简单理论探究与实验阶段,尚未形成成熟可靠的理论对实际设计和应用进行指导。在阻尼颗粒未发生堆积时,考虑阻尼颗粒与阻尼器腔体之间的碰撞过程和摩擦效应,构建一种颗粒阻尼器-单自由度结构系统力学模型,并求得该力学模型在简谐激励下位移响应的解析解。该模型能够充分反映颗粒阻尼器的碰撞和非碰撞过程,其相轨迹可以体现颗粒阻尼器的复杂非线性特征。通过单层钢框架在简谐激励下的电磁振台试验对颗粒阻尼器的理论及运动特性进行验证,证明该理论模型的合理性和解析结果的正确性。最后对颗粒阻尼器进行颗粒质量、激振幅值、激振频率和阻尼颗粒运动间隙的参数分析,并与已有冲击阻尼器模型进行对比,结果表明所构建的力学模型能更加合理地评价颗粒阻尼器的减振性能。
The research and application of particle damper in civil engineering is simply in a theoretical and experimental stage because of the high nonlinear characteristics and complex factors, and no more mature and reliable theory has been formed to guide the design and application in actual civil engineering. When the damping particles are not accumulated, considering the collision process and friction effect between particles and chamber,a mechanical model of particle damper-SDOF system is constructed. The analytical solution of the displacement response of the theoretical model under harmonic excitation is obtained. The mechanical model could fully reflect the collision and non-collision process of particle dampers, and the phase trajectories could reflect the complex nonlinear characteristics of particle dampers. The rationality of the model and the correctness of the analytical results are proved by the verification of the hypothesis of the particle damper and the electromagnetic shaking table test of a single steel frame under simple harmonic excitation. Finally, the parameters of the particle dampers are analyzed in terms of particle size, excitation amplitude, excitation frequency and damping particle motion gap.Moreover, compared with the existing model of impact dampers, the results show that the mechanical model is more reasonable for evaluating the damping performance of particle damper.
The research and application of particle damper in civil engineering is simply in a theoretical and experimental stage because of the high nonlinear characteristics and complex factors, and no more mature and reliable theory has been formed to guide the design and application in actual civil engineering. When the damping particles are not accumulated, considering the collision process and friction effect between particles and chamber,a mechanical model of particle damper-SDOF system is constructed. The analytical solution of the displacement response of the theoretical model under harmonic excitation is obtained. The mechanical model could fully reflect the collision and non-collision process of particle dampers, and the phase trajectories could reflect the complex nonlinear characteristics of particle dampers. The rationality of the model and the correctness of the analytical results are proved by the verification of the hypothesis of the particle damper and the electromagnetic shaking table test of a single steel frame under simple harmonic excitation. Finally, the parameters of the particle dampers are analyzed in terms of particle size, excitation amplitude, excitation frequency and damping particle motion gap.Moreover, compared with the existing model of impact dampers, the results show that the mechanical model is more reasonable for evaluating the damping performance of particle damper.
引文
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[22]闫维明,许维炳,王瑾,等.调谐型颗粒阻尼器简化力学模型及其参数计算方法研究与减震桥梁试验[J].工程力学,2014,31(6):79―84.Yan Weiming,Xu Weibing,Wang Jin,et al.Experimental and theoretical research on the simplified mechanical model of a tuned particle damper,its parameter determination method and earthquake-induced vibration control of bridge[J].Engineering Mechanics,2014,31(6):79―84.(in Chinese)
[23]Papalou A.Performance of particle dampers under random excitation[J].Journal of Vibration&Acoustics,1996,118(4):614―621.
[24]Johnson K L.Contact mechanics[M].UK:Cambridge University Press,1985.
[25]Soong T T,Dargush G F.Passive energy dissipation systems in structural engineering[M].Wiley&Sons,Incorporated,John,1997.
[26]Yan Weiming,Xu Weibing,Wang Jin.Experimental research on the effects of a tuned particle damper on a viaduct system under seismic loads[J].Journal of Bridge Engineering,2014,19(3):1―10.
[27]赵文礼,周晓军.碰撞阻尼器系统的分岔、混沌与控制[J].振动工程学报,2007,20(2):161―167.Zhao Wenli,Zhou Xiaojun.Bifurcation,chaos and control of vibration systems with impact damper[J].Journal of Vibration Engineering,2007,20(2):161―167.(in Chinese)
[2]Xu Z,Wang M Y,Chen T.A particle damper for vibration and noise reduction[J].Journal of Sound and Vibration,2004,270(4/5):1033―1040.
[3]Bai X M,Shah B,Keer L M,et al.Particle dynamics simulations of a piston-based particle damper[J].Powder Technology,2009,189(1):115―125.
[4]Li K,Darby A P.A buffered impact damper for multi-degree-of-freedom structural control[J].Earthquake Engineering&Structural Dynamics,2008,37(13):1491―1510.
[5]Xiao W,Li J,Wang S,et al.Study on vibration suppression based on particle damping in centrifugal field of gear transmission[J].Journal of Sound and Vibration,2016,366(6):62―80.
[6]Masri S F,Caughey T K.On the stability of the impact damper[J].Journal of Applied Mechanics,1966,33(3):586―592.
[7]丁文镜.减振理论[M].北京:清华大学出版社,2014.Ding Wenjing.Vibration damping theory[M].Beijing:Tsinghua University Press,2014.(in Chinese)
[8]Papalou A,Masri S F.Response of impact dampers with granular materials under random excitation[J].Earthquake Engineering&Structural Dynamics,2015,25(3):253―267.
[9]Papalou A,Masri S F.An experimental investigation of particle dampers under harmonic excitation[J].Journal of Vibration and Control,1998,4(4):361―379.
[10]Wu C Y,Li L Y,Thornton C.Energy dissipation during normal impact of elastic and elastic-plastic spheres[J].International Journal of Impact Engineering,2005,32(1/2/3/4):593―604.
[11]Lu Z,Masri S F,Lu X.Parametric studies of the performance of particle dampers under harmonic excitation[J].Structural Control&Health Monitoring,2011,18(1):79―98.
[12]Lu Z,Lu X,Masri S F.Studies of the performance of particle dampers under dynamic loads[J].Journal of Sound and Vibration,2010,329(26):5415―5433.
[13]Lu Z,Masri S F,Lu X.Studies of the performance of particle dampers attached to a two-degrees-of-freedom system under random excitation[J].Journal of Vibration and Control,2011,17(10):1454―1471.
[14]Lu Z,Lu X,Lu W,et al.Shaking table test of the effects of multi-unit particle dampers attached to an MDOFsystem under earthquake excitation[J].Earthquake Engineering&Structural Dynamics,2012,41(5):987―1000.
[15]鲁正,吕西林.颗粒阻尼器减震控制的数值模拟[J].同济大学学报(自然科学版),2013,41(8):1140―1144.Lu Zheng,LüXilin.Numerical simulation of vibration control effects of particle dampers[J].Journal of Tongji University(Natural Science),2013,41(8):1140―1144.(in Chinese)
[16]鲁正,陈筱一,王佃超,等.颗粒调谐质量阻尼器减震控制的数值模拟[J].振动与冲击,2017,36(3):46―50.Lu Zheng,Chen Xiaoyi,Wang Dianchao,et al.Numerical simulation for vibration reduction control of particle tuned mass damper[J].Journal of Vibration and Shock,2017,36(3):46―50.(in Chinese)
[17]Saeki M.Impact damping with granular materials in a horizontally vibrating system[J].Journal of Sound and Vibration,2002,251(1):153―161.
[18]程杨.颗粒阻尼参数的试验研究[D].江苏:扬州大学,2016.Chen Yang.Experimental study on the parameters of particle damper[D].Jiangsu:Yangzhou University,2016.(in Chinese)
[19]闫维明,王瑾,许维炳.基于单自由度结构的颗粒阻尼减振机理试验研究[J].土木工程学报,2014(增刊1):76―82.Yan Weiming,Wang Jin,Xu Weibing.Experimental research on the control mechanism of particle damping based on a single degree of freedom structure[J].China Civil Engineering Journal,2014,(Suppl 1):76―82.(inChinese)
[20]闫维明,谢志强,张向东,等.隔舱式颗粒阻尼器在沉管隧道中的减震控制试验研究[J].振动与冲击,2016,35(17):7―12.Yan Weiming,Xie Zhiqiang,Zhang Xiangdong,et al.Tests for compartmental particle damper’s a seismic control in an immersed tunnel[J].Journal of Vibration and Shock,2016,35(17):7―12.(in Chinese)
[21]闫维明,张向东,黄韵文.基于颗粒阻尼技术的结构减振控制[J].北京工业大学学报,2012,38(9):1316―1320.Yan Weiming,Zhang Xiangdong,Huang Yunwen.Structure vibration control based on particle damping technology[J].Journal of Beijing University of Technology,2012,38(9):1316―1320.(in Chinese)
[22]闫维明,许维炳,王瑾,等.调谐型颗粒阻尼器简化力学模型及其参数计算方法研究与减震桥梁试验[J].工程力学,2014,31(6):79―84.Yan Weiming,Xu Weibing,Wang Jin,et al.Experimental and theoretical research on the simplified mechanical model of a tuned particle damper,its parameter determination method and earthquake-induced vibration control of bridge[J].Engineering Mechanics,2014,31(6):79―84.(in Chinese)
[23]Papalou A.Performance of particle dampers under random excitation[J].Journal of Vibration&Acoustics,1996,118(4):614―621.
[24]Johnson K L.Contact mechanics[M].UK:Cambridge University Press,1985.
[25]Soong T T,Dargush G F.Passive energy dissipation systems in structural engineering[M].Wiley&Sons,Incorporated,John,1997.
[26]Yan Weiming,Xu Weibing,Wang Jin.Experimental research on the effects of a tuned particle damper on a viaduct system under seismic loads[J].Journal of Bridge Engineering,2014,19(3):1―10.
[27]赵文礼,周晓军.碰撞阻尼器系统的分岔、混沌与控制[J].振动工程学报,2007,20(2):161―167.Zhao Wenli,Zhou Xiaojun.Bifurcation,chaos and control of vibration systems with impact damper[J].Journal of Vibration Engineering,2007,20(2):161―167.(in Chinese)