基于多尺度方法的带颗粒阻尼悬臂梁自由振动半解析分析
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摘要
被动式颗粒阻尼器原理简单、性能优越,广泛应用于结构减震领域。极端环境容易激起结构的高频振动,颗粒阻尼的非线性特性使得多模态振动的减振特性相互耦合。采用模态综合法分析自由端带集中质量块的悬臂梁、离散单元法模拟颗粒阻尼器中颗粒集的运动,基于多尺度分析的球-墙耦合模型建立了揭示结构多模态振动条件下颗粒阻尼减振机理的半解析分析模型。分析表明,颗粒阻尼器具有良好的减震效果,减振性能受结构振动模态影响很大。与单一模态振动减振性能相比,多阶模态振动同时存在时,低阶模态幅值的衰减出现了滞后,而高阶模态幅值的衰减则明显加快。因此,采用单一模态获得的等效阻尼比不足以表征复杂振动条件下颗粒阻尼器的减振性能。
Passive particle damper is characterized by simple principle and well behavior and is widely used as structural damping device.In severe environment,the high-frequency vibration of structure can be easily excited and the attenuation characteristics of multi-mode oscillation are coupled because of the nonlinear character of particle damping.To reveal the mechanism of this phenomenon,the cantilever beam with concentrated mass at free end was modelled by modal synthesis method and the motion of particle assembly was simulated by discrete element method.Then,a semi-analytical model was established based on the ball-wall coupling in the light of multiscale theory.Numerical analysis indicates that particle damper is a very effective damping device and the behavior of damper is related to the mode of vibration.In multiorder modes vibration,compared with signle-mode oscillation,the amplitude attenuation of low-order-mode is delayed,while the amplitude attenuation of high-order-mode is quickened.It can be concluded that the equivalent damping ratio for single-mode vibration can't represent the capacity of particle damping in complex vibration condition.
Passive particle damper is characterized by simple principle and well behavior and is widely used as structural damping device.In severe environment,the high-frequency vibration of structure can be easily excited and the attenuation characteristics of multi-mode oscillation are coupled because of the nonlinear character of particle damping.To reveal the mechanism of this phenomenon,the cantilever beam with concentrated mass at free end was modelled by modal synthesis method and the motion of particle assembly was simulated by discrete element method.Then,a semi-analytical model was established based on the ball-wall coupling in the light of multiscale theory.Numerical analysis indicates that particle damper is a very effective damping device and the behavior of damper is related to the mode of vibration.In multiorder modes vibration,compared with signle-mode oscillation,the amplitude attenuation of low-order-mode is delayed,while the amplitude attenuation of high-order-mode is quickened.It can be concluded that the equivalent damping ratio for single-mode vibration can't represent the capacity of particle damping in complex vibration condition.
引文
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[2]Mao K M,Wang M Y,Xu Z W,et al.DEM simulation ofparticle damping[J].Power Technology,2004,142(2-3):154-165.
[3]Friend R D,Kinra V K.Particle impact damping[J].Journal of Sound and Vibration,2000,233(1):93-118.
[4]夏兆旺,单颖春,刘献栋.基于悬臂梁的颗粒阻尼实验[J].航空动力学报,2007,22(10):1737-1741.XIA Zhao-wang,SHAN Ying-chun,LIU Xian-dong.Experimental research on particle damping of cantilever beam[J].Journal of Aerospace Power,2007,22(10):1737-1741.
[5]Cundall P A,Strack O D L.A discrete numerical model forgranular assemblies[J].Geotechnique,1979,29(1):47-65.
[6]胡溧,黄其柏,何雪松.非阻塞性颗粒阻尼的离散元法[J].华中科技大学学报:自然科学版,2008,36(7):81-84.HU Li,HUANG Qi-bai,HE Xue-song.A non-obstructiveparticle damping model of DEM[J].Journal of HuazhongUniversity of Science and Technology:Natural ScienceEdition,2008,36(7):81-84.
[7]段勇,陈前,周宏伟.垂直简谐激励下颗粒阻尼耗能特性的仿真研究[J].振动与冲击,2009,28(2):28-31.DUAN Yong,CHEN Qian,ZHOU Hong-wei.Simulationinvestigation on particle damping for its characteristic of losspower under vertical excitation[J].Journal of Vibration andShock,2009,28(2):28-31.
[8]夏兆旺,温华兵,刘献栋.颗粒阻尼器结构振动特性耦合算法仿真与试验[J].农业机械学报,2011,42(8):26-29.XIA Zhao-wang,WEN Hua-bing,LIU Xian-dong.Couplingalogorithm simulation and experiment of structure vibrationcharacteristics for particle dampers[J].Transactions of theChinese Society of Agricultural Machinery,2011,42(8):26-29.
[9]谭德昕,刘献栋,单颖春.颗粒阻尼减震器对板扭转振动减震的仿真研究[J].系统仿真学报,2011,23(8):1594-1597.TAN De-xin,LIU Xian-dong,SHAN Ying-chun.Simulationof applying particle damper to torsion vibration of plate[J].Journal of System Simulation,2011,23(8):1594-1597.
[10]Lu Z,Lu X,Masri S F.Studies of the performance ofparticle dampers under dynamic loads[J].Journal of Soundand Vibration,2010,329(26):5415-5433.
[11]Simonian S S,Camelo V S,Brennan S,et al.Disturbancesuppression using particle dampers[C].49th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,andMaterials Conference,2008,Schaumburg IL.
[12]Elmekati A,Shamy U E.A practical co-simulation approachfor multiscale analysis of geotechnical systems[J].Computersand Geotechnics,2010,37(4):494-503.
[13]Bai X M,Shah B,Keer L M,et al.Particle dynamicssimulations of a piston-based particle damper[J].PowderTechnology,2009,189(1):115-125.