基于惯容负刚度动力吸振器的梁响应最小化

摘要
图/表
参考文献(26)
相关文章 (15)

全文: PDF (1464 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要提出了两种新型的被动振动控制结构，即含有惯容器和负刚度的动力吸振器振动控制结构，并抑制梁的横向振动。在只考虑一阶模态函数情况下，使用固定点理论推导出了这两种新型动力吸振器的最优控制参数解析表达式。在此基础上，将两种不同的基于惯容负刚度的新型动力吸振器(模型1和模型2)分别与传统动力吸振器在不同质量比下进行了对比分析，数值结果表明，基于惯容负刚度的动力吸振器比传统动力吸振器对梁的振动控制更有效。对于质量比小的情况，模型2比模型1具有更好的减振效果。但是，质量比或者惯容质量比较大时，会导致模型2的最优负刚度比大于0，此时模型2的最优参数不适用。此外，还简要讨论了质量比和惯性质量比对最优系统参数的影响。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	陈杰1
	孙维光2
	吴杨俊1
	张立民1
	贺小龙3

关键词 ：振动控制, 惯容, 负刚度, 梁, 固定点理论

Abstract：Two new types of passive vibration control structures were proposed, namely the vibration control structure of the dynamic vibration absorber with inerter and negative stiffness, and the transverse vibration of the beam was suppressed.In the case of considering only the first-order modal function, the analytical expressions of the optimal control parameters of the two new dynamic absorbers can be derived using the fixed point theory.On this basis, two kinds of new dynamic absorbers based on inerter and negative stiffness (model 1 and model 2) were compared with the traditional dynamic absorbers under different mass ratios.The numerical results show that the dynamic absorber based on inerter and negative stiffness is more effective than the traditional dynamic absorber in vibration control of beams.For the case of small mass ratio, model 2 has better vibration reduction effect than model 1.However, when the mass ratio or inerter mass ratio is large, the optimum negative stiffness ratio of model 2 is greater than 0, and the optimum parameters of model 2 will not be available.In addition, the effects of mass ratio and inerter mass ratio on the optimal system parameters are briefly discussed.

Key words： vibration control inerter negative stiffness beam fixed-point theory

收稿日期: 2019-09-24 出版日期: 2020-04-15

引用本文:

陈杰1，孙维光2，吴杨俊1，张立民1，贺小龙3. 基于惯容负刚度动力吸振器的梁响应最小化[J]. 振动与冲击, 2020, 39(8): 15-22.
CHEN Jie1，SUN Weiguang2，WU Yangjun1，ZHANG Limin1，HE Xiaolong3. Minimization of beam response using inerter-based dynamic vibration absorber with negative stiffness. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(8): 15-22.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I8/15

［1］倪振华.振动力学［M］.西安：西安交通大学出版社, 1989. ［2］PREUMONT A.Vibration control of active structures ［M］.Dordrecht: Kluwer Academic Pub, 2002. ［3］DEN HARTOG J P.Mechanical vibrations［M］.New York: Dover Publication Inc, 1985. ［4］ASAMI T, NISHIHARA O, BAZ A M.Analytical solutions to H∞ and H2 optimization of dynamic vibration absorbers attached to damped linear systems［J］.Journal of Vibration and Acoustics, 2002, 124(2): 284-295. ［5］纪晗, 熊世树, 袁涌.基于负刚度原理的结构隔振效果分析［J］.华中科技大学学报 (自然科学版), 2010, 38(2): 76-79. JI Han, XIONG Shishu, YUAN Yong.Analyzing vibration isolation effect of structures using negative stiffness principle［J］.Journal of Huazhong University of Science and Technology (Natural Science), 2010, 38(2): 76-79. ［6］SIMTH M C.Synthesis of mechanical: the inerter［J］.IEEE Transaction on Automatic Control, 2002, 47(10): 1648-1662. ［7］聂佳梅，张孝良，江浩斌，等.惯容器模型结构探索［J］.机械设计与研究, 2012,28(1): 29-32. NIE Jiamei, ZHANG Xiaoliang, JIANG Haobin, et al.Research on the inerter structure［J］.Journal of Mechanical Design and Research, 2012, 28(1): 29-32. ［8］SHEN Y J, PENG H B, LI X H, et al.Analytically optimal parameters of dynamic vibration absorber with negative stiffness［J］.Mechanical Systems and Signal Processing, 2017, 85: 193-203. ［9］彭海波，申永军，杨绍普.一种含负刚度元件的新型动力吸振器的参数优化［J］.力学学报, 2015,47(2): 320-327. PENG Haibo, SHEN Yongjun, YANG Shaopu.Parameters optimization of a new type of dynamic vibration absorber with negative stiffness［J］.Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 320-327. ［10］王孝然，申永军，杨绍普，等.含负刚度元件的三要素型动力吸振器的参数优化［J］.振动工程学报, 2017,30(2): 177-184. WANG Xiaoran, SHEN Yongjun, YANG Shaopu, et al.Parameter optimization of three-element type dynamic vibration absorber with negative stiffness［J］.Journal of Vibration Engineering, 2017, 30(2): 177-184. ［11］WANG X R, LIU X D, SHAN Y C, et al.Analysis and optimization of the novel inerter-based dynamic vibration absorbers［J］.IEEE Access, 2018, 6: 33169-33182. ［12］王孝然，申永军，杨绍普.接地式三要素动力吸振器的H∞优化［J］.动力学与控制学报, 2016, 14(5): 448-453. WANG Xiaoran, SHEN Yongjun, YANG Shaopu.H∞ optimization of the grounded three-element typer dynamic vibration absorber［J］.Journal of Dynamic and Control, 2016, 14(5): 448-453. ［13］李壮壮，申永军，杨绍普，等.基于惯容-弹簧-阻尼的结构减振研究［J］.振动工程学报, 2018,31(6): 1061-1067. LI Zhuangzhuang, SHEN Yongjun, YANG Shaopu, et al.Study on vibration mitigation based on inerter-spring-damping structure［J］.Journal of Vibration Engineering, 2018, 31(6): 1061-1067. ［14］HU Y, CHEN M Z Q, SHU Z.Passive vehicle suspensions employing inerters with multiple performance requirements［J］.Journal of Sound and Vibration, 2014, 333: 2212-2225. ［15］CHEN M Z Q, HU Y, HUANG L, et al.Influence of inerter on natural frequencies of vibration systems［J］.Journal of Sound and Vibration, 2014, 333: 1874-1887. ［16］LEWIS T D, JIANG J Z, NEILD S A, et al.Using an inerter-based suspension to improve both passenger comfort and track wear in railway vehicles［J］.Vehicle System Dynamics, 2020, 58(3): 472-493. ［17］陈龙，杨晓峰，汪若尘，等．基于二元件ISD结构隔振机理的车辆被动悬挂设计与性能研究［J］．振动与冲击, 2013, 32(6): 90-95. CHEN Long, YANG Xiaofeng, WANG Ruochen, et al.Design and performance study of vehicle passive suspension based on two-element inerter-spring-damper structure vibration isolation mechanism［J］.Journal of Vibration and Shock, 2013, 32(6): 90-95. ［18］杜甫，毛明，陈轶杰，等．基于动力学模型与参数优化的ISD悬挂结构设计及性能分析［J］．振动与冲击, 2014, 33(6): 59-65. DU Fu, MAO Ming, CHEN Yijie, et al.Structure design and performance analysis of inerter-spring-damper suspension structure based on dynamic model and parameter optimization［J］.Journal of Vibration and Shock, 2014, 33(6): 59-65. ［19］WANG F C, LIAO M K, LIAO B H, et al. The performance improvements of train suspension systems with mechanical networks employing inerters［J］.Vehicle System Dynamic, 2009, 47: 805-830. ［20］KELTIE R F, CHENG C C.Vibration reduction of a mass-loaded beam［J］.Journal of Sound and Vibration, 1995, 187: 213-228. ［21］SAMANI F S, PELLICANO F.Vibration reduction on beams subjected to moving loads using linear and nonlinear dynamic absorbers［J］.Journal of Sound and Vibration, 2009, 325: 742-754. ［22］JACQUOT R G.Optimal dynamic vibration absorbers for general beam systems［J］.Journal of Sound and Vibration, 1978, 60(4): 535-542. ［23］JACQUOT R G.The spatial average mean square motion as an objective function foroptimizing damping in damped modified systems［J］.Journal of Sound and Vibration, 2003, 259(4): 955-965. ［24］JACQUOT R G.Optimal damper location for randomly forced cantilever beams［J］.Journal of Sound and Vibration, 2004, 269(3/4/5): 623-632. ［25］JIN X L, CHEN M Z Q, HUANG Z L.Minimization of the beam response using inerter-based passive vibration control configurations［J］.International Journal of Mechanical Sciences, 2016,119: 80-87. ［26］邢子康，申永军，李向红.接地式三要素型动力吸振器性能分析［J］.力学学报，2019, 51(5): 1466-1475. XING Zikang, SHEN Yongjun, LI Xianghong.Performance analysis of grounded three-element dynamic vibration absorber［J］.Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1466-1475.