具有干摩擦的简支梁振动特性与减振机理
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- 英文论文题名：Vibration Characteristics and Vibration Suppression Mechanism of the Simply Supported Beam with Dry Friction
- 论文作者：赵峰 ; 王良文 ; 罗国富 ; 曹树谦
- 英文论文作者：Zhao Feng ; Wang Liangwen ; Luo Guofu ; Cao Shuqian ; School of Mechatronic Engineering ; Zhengzhou University of Light Industry ; Department of Mechanics ; Tianjin University ; Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control
- 年：2016
- 作者机构：郑州轻工业学院机电工程学院;天津大学力学系;天津市非线性动力学与控制重点实验室;
- 论文关键词：简支梁 ; 干摩擦 ; 振动特性 ; 减振器
- 英文论文关键词：Simply supported beam ; Dry friction ; Vibration characteristics ; Vibration absorber
- 会议召开时间：2016-08-12
- 会议录名称：第十六届全国模态分析与试验学术会议论文集
- 语种：中文
- 分类号：TB123
- 学会代码：ZGZH
- 会议名称：第十六届全国模态分析与试验学术会议
- 会议地点：中国天津
- 主办单位：中国振动工程学会模态分析与试验专业委员会
- 学会名称：中国振动工程学会
- 页数：9
- 文件大小：1052k
- 原文格式：D
- 会议级别：全国
摘要
简支梁结构在扰动下将产生振动,采用干摩擦组成的减振器并从模态角度可揭示简支梁结构振动抑制机理。针对干摩擦简支梁和无摩擦简支梁等效模型,分别采用拉格朗日第一、二类方程建立运动方程,获得频率与能量的解析式;进而基于能量等效思想,获得摩擦简支梁等效自然频率解析式。随后对获得的等效自然频率解析式进行数值方法验证,第一阶自然频率解析结果与数值结果随着摩擦力的增大而降低。另外,摩擦力和摩擦位置可很大程度上改变简支梁自然频率,并通过改变系统的能量进一步影响结构的减振特性;模态振型是振动抑制的重要影响因素。
Vibration will be generated on simply supported beam under perturbance conditions. The vibration can be suppressed by using the absorber composed of dry friction,and the modal method is helpful to research the mechanism of the vibration suppression. The lagrange's equations of the first and second kinds are used in the simply supported beam with dry friction and an equivalent model,separately. The analytical equation between frequency and energy can be deduced. Based on the equivalent method of energy,the natural frequencies of the simply supported beam with dry friction are obtained with an analytical equation. Then,the analytical equation of natural frequencies is verified by numerical method. The natural frequencies of the first order computed by analytical method and numerical method are all decreasing with the increase of amplitude value of dry friction. In addition,the amplitude of dry friction and its location can change the natural frequencies of the simply supported beam to a large extent. This feature can change the system's energy,which furtherly controls the characteristic of vibration suppression of the frictional beam. The mode shape is also one important factor of vibration suppression research.
Vibration will be generated on simply supported beam under perturbance conditions. The vibration can be suppressed by using the absorber composed of dry friction,and the modal method is helpful to research the mechanism of the vibration suppression. The lagrange's equations of the first and second kinds are used in the simply supported beam with dry friction and an equivalent model,separately. The analytical equation between frequency and energy can be deduced. Based on the equivalent method of energy,the natural frequencies of the simply supported beam with dry friction are obtained with an analytical equation. Then,the analytical equation of natural frequencies is verified by numerical method. The natural frequencies of the first order computed by analytical method and numerical method are all decreasing with the increase of amplitude value of dry friction. In addition,the amplitude of dry friction and its location can change the natural frequencies of the simply supported beam to a large extent. This feature can change the system's energy,which furtherly controls the characteristic of vibration suppression of the frictional beam. The mode shape is also one important factor of vibration suppression research.
引文
[1]朱志辉,王力东,杨乐,等.轨道不平顺短波分量对列车-简支梁桥耦合振动的影响.湖南大学学报(自然科学版),2016,43(1):53-60.
[2]李小珍,张志俊,刘全民.任意移动荷载列作用下简支梁桥竖向振动响应解析分析.振动与冲击,2012,31(20):137-142.
[3]酆庆增.简支梁大挠度非线性振动中的突变和混沌.计算物理,1987,4(2):129-136.
[4]高原文,周又和,郑晓静.横向磁场激励下铁磁梁式板的混沌运动分析.力学学报,2002,34(1):101-108.
[5]P Museros,M D Martinez-Rodrigo.Vibration control of simply supported beams under moving loads using fluid viscous damper,Journal of Vibration and Control,2007,300:292-315.
[6]李慧乐,夏禾,郭薇薇.简支梁在列车荷载下的共振与消效应.振动工程学报,2014,27(2):172-179.
[7]C Nicola,L Walter,V Fabrizio.Hysteretic tuned mass dampers for structural vibration mitigation.Journal of Sound and Vibration,2014,333:1302-1318.
[8]Den Hartog J P.Forced vibrations with combined viscous and coulomb damping[J].Phil.Mag.S.7,1930,9(59):801-817.
[9]赵峰,曹树谦,于跃斌,等.干摩擦双层梁的工作模态实验方法[J].振动、测试与诊断,2013,33(6):971-976.
[10]严天宏,郑钢铁,黄文虎.由摩擦阻尼铰实现桁架结构的被动减振研究[J].航空学报,1999,20(1):17-21.
[11]贾尚帅,丁千.刹车系统的摩擦自激振动和控制[J].工程力学,2012,(03):252-256.
[12]丁千,陈予恕.转子碰摩运动的非稳态分析[J].航空动力学报,2000,(02):191-195.
[13]陈予恕,吴志强.非线性模态理论的研究进展[J].力学进展,1997,27(3):289-299.
[14]Vakakis A F,Bergman L A,McF arland D M,et al.Current efforts towards a non-linear system identification methodology of broad applicability[J].Proceedings of the Institution of Mechanical Engineers C:Journal of Mechanical Engineering Science,2011,000:1-19.
[15]Whiteman W E,Ferri A A.Displacement-dependent dry friction damping of a beam-like structure[J].Journal of Sound and Vibration,1996,198(3):313-329.
[16]Ren Y S,Qin H Z,Zhao Z L.Nonlinear vibration analysis of a beam with dry friction at the supports[J].Mechanics Research Communications,1999,26(1):83-89.
[17]Whiteman W W,Ferri A A.Multi-mode analysis of beam-like structures subjected to displacement-dependent dry friction damping.Journal of Sound and Vibration,1997,207(3):403-418.
[18]Ferri A A,Dowell E H.Frequency domain solutions to multi-degree-of-freedom,dry friction damped systems[J].Journal of Sound and Vibration,1988,124(2):207-224.
[19]Dowell E H,Schwartz H B.Forced response of a cantilever beam with a dry friction damper attached,part 1:theory[J].Journal of Sound and Vibration,1983,91(2):255-267.
[20]Young J G,Kim Y H,Chang H G.An analysis of the Behavior of a Simply Supported Beam with a dry Friction Damper Attached[J].Applied Acoustics,1998,55(1):31-41.
[21]郝淑英,陈予恕,张琪昌.连接结构松动对系统非线性动力学特性的影响[J].天津大学学报,2001,34(4):452-454.
[22]Dowell E H.The behavior of a linear,damped modal system with a non-linear spring-mass-dry friction damper system attached[J].Journal of Sound and Vibration,1983,89(1):65-84.
[23]Ferri A A,Whiteman W E.Free response of a system with negative viscous damping and displacementdependent dry friction damping[J].Journal of Sound and Vibration,2007,306:400-418.
[24]Ostachowicz W M.A discrete linear beam model to investigate the nonlinear effects of slip friction[J].Computer and Structures,1990,36(4):721-728.
[25]Poudou O J.Modeling and analysis of the dynamics of dry-friction-damped structural systems[D].University of Michigan,2007.
[26]Dowell E H.Damping in beams and plates due to slipping at the support boundaries[J].Journal of Sound and Vibration,1986,105(2):243-253.
[27]Zhao F,Cao S Q,Yu Y B,et al.Theoretical study of the natural frequencies of a cantilever beam under dry friction.Journal of Vibration and Control,2015,on line.
[28]Kerschen G,Worden K,Vakakis A F,et al.Past,present and future of nonlinear system identification in structural dynamics[J].Mechanical Systems and Signal Processing,2006,20(3):505–592.
[2]李小珍,张志俊,刘全民.任意移动荷载列作用下简支梁桥竖向振动响应解析分析.振动与冲击,2012,31(20):137-142.
[3]酆庆增.简支梁大挠度非线性振动中的突变和混沌.计算物理,1987,4(2):129-136.
[4]高原文,周又和,郑晓静.横向磁场激励下铁磁梁式板的混沌运动分析.力学学报,2002,34(1):101-108.
[5]P Museros,M D Martinez-Rodrigo.Vibration control of simply supported beams under moving loads using fluid viscous damper,Journal of Vibration and Control,2007,300:292-315.
[6]李慧乐,夏禾,郭薇薇.简支梁在列车荷载下的共振与消效应.振动工程学报,2014,27(2):172-179.
[7]C Nicola,L Walter,V Fabrizio.Hysteretic tuned mass dampers for structural vibration mitigation.Journal of Sound and Vibration,2014,333:1302-1318.
[8]Den Hartog J P.Forced vibrations with combined viscous and coulomb damping[J].Phil.Mag.S.7,1930,9(59):801-817.
[9]赵峰,曹树谦,于跃斌,等.干摩擦双层梁的工作模态实验方法[J].振动、测试与诊断,2013,33(6):971-976.
[10]严天宏,郑钢铁,黄文虎.由摩擦阻尼铰实现桁架结构的被动减振研究[J].航空学报,1999,20(1):17-21.
[11]贾尚帅,丁千.刹车系统的摩擦自激振动和控制[J].工程力学,2012,(03):252-256.
[12]丁千,陈予恕.转子碰摩运动的非稳态分析[J].航空动力学报,2000,(02):191-195.
[13]陈予恕,吴志强.非线性模态理论的研究进展[J].力学进展,1997,27(3):289-299.
[14]Vakakis A F,Bergman L A,McF arland D M,et al.Current efforts towards a non-linear system identification methodology of broad applicability[J].Proceedings of the Institution of Mechanical Engineers C:Journal of Mechanical Engineering Science,2011,000:1-19.
[15]Whiteman W E,Ferri A A.Displacement-dependent dry friction damping of a beam-like structure[J].Journal of Sound and Vibration,1996,198(3):313-329.
[16]Ren Y S,Qin H Z,Zhao Z L.Nonlinear vibration analysis of a beam with dry friction at the supports[J].Mechanics Research Communications,1999,26(1):83-89.
[17]Whiteman W W,Ferri A A.Multi-mode analysis of beam-like structures subjected to displacement-dependent dry friction damping.Journal of Sound and Vibration,1997,207(3):403-418.
[18]Ferri A A,Dowell E H.Frequency domain solutions to multi-degree-of-freedom,dry friction damped systems[J].Journal of Sound and Vibration,1988,124(2):207-224.
[19]Dowell E H,Schwartz H B.Forced response of a cantilever beam with a dry friction damper attached,part 1:theory[J].Journal of Sound and Vibration,1983,91(2):255-267.
[20]Young J G,Kim Y H,Chang H G.An analysis of the Behavior of a Simply Supported Beam with a dry Friction Damper Attached[J].Applied Acoustics,1998,55(1):31-41.
[21]郝淑英,陈予恕,张琪昌.连接结构松动对系统非线性动力学特性的影响[J].天津大学学报,2001,34(4):452-454.
[22]Dowell E H.The behavior of a linear,damped modal system with a non-linear spring-mass-dry friction damper system attached[J].Journal of Sound and Vibration,1983,89(1):65-84.
[23]Ferri A A,Whiteman W E.Free response of a system with negative viscous damping and displacementdependent dry friction damping[J].Journal of Sound and Vibration,2007,306:400-418.
[24]Ostachowicz W M.A discrete linear beam model to investigate the nonlinear effects of slip friction[J].Computer and Structures,1990,36(4):721-728.
[25]Poudou O J.Modeling and analysis of the dynamics of dry-friction-damped structural systems[D].University of Michigan,2007.
[26]Dowell E H.Damping in beams and plates due to slipping at the support boundaries[J].Journal of Sound and Vibration,1986,105(2):243-253.
[27]Zhao F,Cao S Q,Yu Y B,et al.Theoretical study of the natural frequencies of a cantilever beam under dry friction.Journal of Vibration and Control,2015,on line.
[28]Kerschen G,Worden K,Vakakis A F,et al.Past,present and future of nonlinear system identification in structural dynamics[J].Mechanical Systems and Signal Processing,2006,20(3):505–592.