连续参数型动力吸振器吸振效果分析
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摘要
为了提升参数型动力吸振器的吸振效果,文中提出一种用于控制杆纵向模态振动的连续参数型悬臂梁动力吸振器。分析了杆纵振和吸振器弯曲振动的模态参数;建立广义坐标下杆-动力吸振器耦合振动系统的数学模型,得出传到基础的力与激振力传递率的解析表达式,得到连续参数型动力吸振器进行模态振动控制需满足的条件,给出吸振器的设计实例;分析了吸振器的吸振效果,探讨了安装位置对吸振效果的影响。结果表明:连续参数型悬臂梁动力吸振器可同时控制杆的多阶模态振动,并给出有效吸振的频率范围,将吸振安装到杆的前端,可增大有效吸振带宽。
In order to improve the vibration absorption effect of parametric dynamic vibration absorbers,this paper presents a continuous parametric cantilever beam dynamic vibration absorber for controlling the longitudinal mode vibration of a rod.First,the modal parameters of rod longitudinal vibration and absorber bending vibration were analyzed.Secondly,the mathematical model of the rod-dynamic vibration absorber coupled with a vibration system under the generalized coordinates was established.The analytic expression of the force transfer rate and the condition for modal vibration control by the continuous parametric dynamic vibration absorber are obtained,on the basis of which one vibration absorber was designed.Finally,its shock absorption and the effect of its mounting position on vibration absorption were analyzed.Simulation results show that the continuous parametric cantilever dynamic vibration absorber can control the multi-order mode vibration of a rod,giving the frequency range of effective vibration absorption and that the installation of the vibration absorber at the front end of the rod can increase the range of effective vibration absorption.
In order to improve the vibration absorption effect of parametric dynamic vibration absorbers,this paper presents a continuous parametric cantilever beam dynamic vibration absorber for controlling the longitudinal mode vibration of a rod.First,the modal parameters of rod longitudinal vibration and absorber bending vibration were analyzed.Secondly,the mathematical model of the rod-dynamic vibration absorber coupled with a vibration system under the generalized coordinates was established.The analytic expression of the force transfer rate and the condition for modal vibration control by the continuous parametric dynamic vibration absorber are obtained,on the basis of which one vibration absorber was designed.Finally,its shock absorption and the effect of its mounting position on vibration absorption were analyzed.Simulation results show that the continuous parametric cantilever dynamic vibration absorber can control the multi-order mode vibration of a rod,giving the frequency range of effective vibration absorption and that the installation of the vibration absorber at the front end of the rod can increase the range of effective vibration absorption.
引文
[1]SHEN Y J,PENG H B,LI X H,et al.Analytically Optimal Parameters of Dynamic Vibration Absorber with Negative Stiffness[J].Mechanical Systems&Signal Processing,2017,85:193.
[2]张洪田,刘志刚,张志华,等.动力吸振技术的现状与发展[J].噪声与振动控制,1996(3):22.ZHANG Hongtian,LIU Zhigang,ZHANG Zhihua,et al.Present Situation and Development of Dynamic Vibration Absorbing Technique[J].Noise and Vibration Control,1996(3):22.(in Chinese)
[3]刘耀宗,郁殿龙,赵宏刚,等.被动式动力吸振技术研究进展[J].机械工程学报,2007,43(3):14.LIU Yaozong,YU Dianlong,ZHAO Honggang,et al.Review of Passive Dynamic Vibration Absorbers[J].Chinese Journal of Mechanical Engineering,2007,43(3):14.(in Chinese)
[4]ASAMI T,NISHIHARA O,BAZ A M.Analytical Solutions to H∞and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems[J].Transactions of the Japan Society of Mechanical Engineers,2002,67(655):597.
[5]李春祥,刘艳霞,王肇民.质量阻尼器的发展[J].力学进展,2003,33(2):194.LI Chunxiang,LIU Yanxia,WANG Zhaomin.A Review of Mass Dampers[J].Advances in Mechanics,2003,33(2):194.(in Chinese)
[6]李春祥,熊学玉,王肇民.结构-MTMD系统的动力特性研究[J].振动与冲击,1999,18(4):50.LI Chunxiang,XIONG Xueyu,WANG Zhaomin.Research on Dynamic Characteristics of a Structure-MT-MD System[J].Journal of Vibration and Shock,1999,18(4):50.(in Chinese)
[7]李春祥.土木工程结构振动控制的最佳多重调谐质量阻尼器模型[J].四川建筑科学研究,2004,30(1):99.LI Chunxiang.Preferable Modeling of Multiple Tuned Mass Dampers for Vibration Control of Structures[J].Sichuan Building Science,2004,30(1):99.(in Chinese)
[8]SNOWDON J C,JONES D I G.Vibration and Shock in Damped Mechanical Systems[J].Journal of Applied Mechanics,1968,36(2):473.
[9]JACQUOT R G,FOSTER J E.Optimal Cantilever Dynamic Vibration Absorbers[J].Journal of Engineering for Industry,1977,99(1):138.
[10]王彦琴,盛美萍,孙进才.变截面梁式动力吸振器的宽带吸振机理[J].振动工程学报,2004,17(4):473.WANG Yanqin,SHENG Meiping,SUN Jincai.Characteristic of Dynamic Vibration Absorber Shaped NonUniform Beam[J].Journal of Vibration Engineering,2004,17(4):473.(in Chinese)
[11]肖和业,盛美萍,雷烨.连续参数型吸振器吸振分析及优化[J].振动、测试与诊断,2012,32(3):447.XIAO Heye,SHENG Meiping,LEI Ye.Analysis and Optimization of Vibration Absorption of Continuous Parameter Vibration Absorbers[J].Journal of Vibration Measurement&Diagnosis,2012,32(3):447.(in Chinese)
[12]RAO S S.机械振动[M].李欣业,张明路,译.4版.北京:清华大学出版社,2009.RAO S S.Mechanical Vibrations[M].LI Xinye,ZHANG Minglu,Translated.4th ed.Beijing:Tsinghua University Press,2009.(in Chinese)
[2]张洪田,刘志刚,张志华,等.动力吸振技术的现状与发展[J].噪声与振动控制,1996(3):22.ZHANG Hongtian,LIU Zhigang,ZHANG Zhihua,et al.Present Situation and Development of Dynamic Vibration Absorbing Technique[J].Noise and Vibration Control,1996(3):22.(in Chinese)
[3]刘耀宗,郁殿龙,赵宏刚,等.被动式动力吸振技术研究进展[J].机械工程学报,2007,43(3):14.LIU Yaozong,YU Dianlong,ZHAO Honggang,et al.Review of Passive Dynamic Vibration Absorbers[J].Chinese Journal of Mechanical Engineering,2007,43(3):14.(in Chinese)
[4]ASAMI T,NISHIHARA O,BAZ A M.Analytical Solutions to H∞and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems[J].Transactions of the Japan Society of Mechanical Engineers,2002,67(655):597.
[5]李春祥,刘艳霞,王肇民.质量阻尼器的发展[J].力学进展,2003,33(2):194.LI Chunxiang,LIU Yanxia,WANG Zhaomin.A Review of Mass Dampers[J].Advances in Mechanics,2003,33(2):194.(in Chinese)
[6]李春祥,熊学玉,王肇民.结构-MTMD系统的动力特性研究[J].振动与冲击,1999,18(4):50.LI Chunxiang,XIONG Xueyu,WANG Zhaomin.Research on Dynamic Characteristics of a Structure-MT-MD System[J].Journal of Vibration and Shock,1999,18(4):50.(in Chinese)
[7]李春祥.土木工程结构振动控制的最佳多重调谐质量阻尼器模型[J].四川建筑科学研究,2004,30(1):99.LI Chunxiang.Preferable Modeling of Multiple Tuned Mass Dampers for Vibration Control of Structures[J].Sichuan Building Science,2004,30(1):99.(in Chinese)
[8]SNOWDON J C,JONES D I G.Vibration and Shock in Damped Mechanical Systems[J].Journal of Applied Mechanics,1968,36(2):473.
[9]JACQUOT R G,FOSTER J E.Optimal Cantilever Dynamic Vibration Absorbers[J].Journal of Engineering for Industry,1977,99(1):138.
[10]王彦琴,盛美萍,孙进才.变截面梁式动力吸振器的宽带吸振机理[J].振动工程学报,2004,17(4):473.WANG Yanqin,SHENG Meiping,SUN Jincai.Characteristic of Dynamic Vibration Absorber Shaped NonUniform Beam[J].Journal of Vibration Engineering,2004,17(4):473.(in Chinese)
[11]肖和业,盛美萍,雷烨.连续参数型吸振器吸振分析及优化[J].振动、测试与诊断,2012,32(3):447.XIAO Heye,SHENG Meiping,LEI Ye.Analysis and Optimization of Vibration Absorption of Continuous Parameter Vibration Absorbers[J].Journal of Vibration Measurement&Diagnosis,2012,32(3):447.(in Chinese)
[12]RAO S S.机械振动[M].李欣业,张明路,译.4版.北京:清华大学出版社,2009.RAO S S.Mechanical Vibrations[M].LI Xinye,ZHANG Minglu,Translated.4th ed.Beijing:Tsinghua University Press,2009.(in Chinese)
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