负刚度时滞反馈控制动力吸振器的反共振优化

摘要
图/表
参考文献(28)
相关文章 (15)

全文: PDF (2453 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要提出一种含接地负刚度弹簧的时滞动力吸振器的反共振峰最小优化方法。首先,研究的模型不考虑时滞位移控制和主系统的阻尼,利用固定点理论得到接地负刚度系统的最优结构参数。其次,考虑优化调节负刚度系数,利用反共振峰最小准则,把反共振点幅值控制在给定的足够小的范围内,得到一组最优结构参数,使得调控的反共振频率频带最宽。再次,调节主系统的阻尼系数,得到最终的一组最优结构参数。最后,通过幅频响应和时间历程响应曲线证明了反共振峰最小准则的正确性,并且将本文结果与其它两种等峰优化的吸振器模型的减振效果进行对比,证明了接地负刚度时滞动力吸振器减振效果优越性。

	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
	代晗
	赵艳影

关键词 ：负刚度, 反共振点, 时滞反馈控制, 动力吸振器

Abstract：In the present paper, an anti-resonance peak minimization criterion (APMC) is studied in the delayed feedback dynamic vibration absorber vibrating system with negative stiffness.Firstly, the first step optimal structural parameters of the negative stiffness grounding system is obtained by using the fixed point theory. In this step, the time-delay positions control and the damping of the main system are not considered, and optimal structural parameters are recorded as the first step optimal structural parameters. Secondly, the second step optimal structural parameters of the system is obtained by using the APMC. In this step, negative stiffness coefficient and delayed feedback control is considered, and the amplitude of the anti-resonance point is controlled in a very small range with wide frequency band of anti-resonance peak. Thirdly, the third step optimal structural parameters of the system is obtained by adjusting the damping coefficient of the main system. Finally, the numerical simulation results of amplitude-frequency and time-history response curves are agree with the analytical results well, and the correctness of APMC can be proved. The results of the present paper are compared with those of the other two models of passive vibration absorbers. The superiority of delayed feedback control with negative stiffness system is proved at the fact of perfect vibration reduction performance.

Key words： negative stiffness anti-resonance point delayed feedback control dynamic vibration absorber

收稿日期: 2020-10-14 出版日期: 2022-02-28

引用本文:

代晗，赵艳影. 负刚度时滞反馈控制动力吸振器的反共振优化[J]. 振动与冲击, 2022, 41(4): 4-13.
DAI Han，ZHAO Yanying. Anti-resonance optimization of dynamic vibration absorbers with negative stiffness and delay feedback control. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(4): 4-13.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I4/4

[1] FRAHM Hermann. Device For Damping Vibrations Of Bodies: US, US0989958[P]. 1909.
[2] DEN HARTOG J P. Mechanical vibrations[M]. 4th. Courier Corporation, 1956: 87-106.
[3] ORMONDROYD J., HARTOG J. P. Den. The theory of dynamic vibration absorber[J]. Journal of Applied Mechanics-Transactions of the Asme, 1928, 50: 9-22.
[4] ASAMI Toshihiko, NISHIHARA Osamu. Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)[J]. Journal of Vibration and Acoustics, 2003, 125(3): 398-405.
[5] NISHIHARA Osamu, ASAMI Toshihiko. Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)[J]. Journal of Vibration and Acoustics, 2002, 124(4): 576-582.
[6] 彭解华，陈树年. 正、负刚度并联结构的稳定性及应用研究[J]. 振动.测试与诊断，1995，15(02): 14-18.
PENG Jie Hua, CHEN Shu Nian. The stability and application of a structure with positive stiffness element and negative stiffness element[J]. Journal of Vibration, Measurement ＆
Diagnosis, 1995, 15(02): 14-18.
[7] 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(02): 320-327
PENG Hai Bo, SHEN Yong Jun, YANG Shao Pu. Parameters optimization of a new type of dynamic vibration absorber with negative stiffness[J]. Chinese Journal of Theoretical and
Applied Mechanics, 2015, 47(02): 320-327.
[8] 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(02): 177-184.
WANG Xiao Ran, SHEN Yong Jun, YANG Shao Pu .etl al. Parameter optimization of three-element type dynamic vibration absorber with negative stiffness[J], Journal of Vibration Engineering ，2017, 30(02): 177-184.
[9] 郝岩，申永军，杨绍普，等. 含负刚度器件的Maxwell模型动力吸振器的参数优化[J]. 振动与冲击，2019，38(04): 20-25.
HAO Yan, SHEN Yong Jun, YANG Shao Pu .etl al. Parameter optimization of a maxwell model dynamic vibration absorber with negative stiffness[J]. Journal of Vibration and Shock, 2019, 38(04): 20-25.
[10] 邢昭阳，申永军，邢海军，等. 一种含放大机构的负刚度动力吸振器的参数优化[J]. 力学学报，2019，51(03): 894-903.
XING Zhao Yang, SHEN Yong Jun, XING Hai Jun .etl al. Parameters optimization of a dynamic vibration absorber with amplifying mechanism and negative stiffness[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(03): 894-903.
[11] 陈杰，孙维光，吴杨俊，等. 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(08): 15-22.
CHEN Jie, SUN Wei Guang, WU Yang Jun .etl al. Minimization of beam response using inerter-based dynamic vibration absorber with negative stiffness[J]. Journal of Vibration and Shock, 2020, 39(08): 15-22.
[12] FLANNELLY William G. Dynamic antiresonant vibration isolator: US, US3445080DA[P]. 1969.
[13] DESJARDINS Rene A., HOOPER W. E. Antiresonant Rotor Isolation for Vibration Reduction[J]. Journal of the American Helicopter Society, 1980, 25(3): 46.
[14] RITA A. D., MCGARVEY Joseph H., JONES Robert. Helicopter Rotor Isolation Evaluation Utilizing the Dynamic Antiresonant Vibration Isolator[J]. Journal of the American Helicopter Society, 1976, 23(1): 22.
[15] 李园园，陈国平，王轲. 直升机旋翼/机身动力反共振隔振器的优化设计[J]. 振动与冲击，2016，35(15): 115-121.
LI Yuan Yuan, CHEN Guo Ping, WANG Ke. Optimization design for dynamic anti-resonance isolators of helicopters' rotor/fuselage[J]. Journal of Vibration and Shock, 2016, 35(15): 115-121.
[16] 周为民，顾仲权. 主动反共振隔振装置的研究(一)理论分析与优化设计[J]. 南京航空航天大学学报，1989，(03): 1-8.
ZHOU Wei Min, GU Zhong Quan. Research on Active Dynamic Antiresonant vibration Isolator-Part 1 Theoretical Analysis and Optimization Design[J]. Journal of Nanjing University of Aeronautics & Astronautics, 1989,(03): 1-8.
[17] 范德礼，吴文敏，董兴建，等. 可调频液压式动力反共振隔振器动力学分析及优化设计[J]. 振动与冲击，2019，38(14): 33-36+47.
FAN De Li, WU Wen Min, DONG Xing Jian .etl al. Dyanmic analysis of a frequency tunable hydraulic anti-resonant vibration isolator and its optimization[J]. Journal of Vibration and Shock, 2019, 38(14): 33-36+47.
[18] 沈安澜，刘续兴，陈静，等. 新型聚焦反共振式主减隔振系统性能分析[J]. 振动与冲击，2018，37(11): 71-79.
SHEN An Lan, LIU Xu Xing, CHEN Jing .etl al. Performance analysis for a new focal anti-resonant gearbox vibration isolation system[J]. Journal of Vibration and Shock, 2018, 37(11): 71-79.
[19] OLGAC N., HOLM-HANSEN B. T. A Novel Active Vibration Absorption Technique: Delayed Resonator[J]. Journal of Sound & Vibration, 1994, 176(1): 93-104.
[20] ZHAO Yan Ying, XU Jian. Effects of delayed feedback control on nonlinear vibration absorber system[J]. Journal of Sound & Vibration, 2007, 308(1-2): 212-230.
[21] MENG Hao, SUN Xiuting, XU Jian .etl al. The generalization of equal-peak method for delay-coupled nonlinear system[J]. Physica D Nonlinear Phenomena, 2020, 403.
[22] SIPAHI Rifat, OLGAC Nejat. Stability Robustness of Retarded LTI Systems with Single Delay and Exhaustive Determination of Their Imaginary Spectra[J]. SIAM Journal on Control and Optimization, 2006, 45(5): 1680-1696.
[23] DIXON A. L. The Eliminant of Three Quantics in two Independent Variables[J]. Proceedings of the London Mathematical Society, 1909, s2-7(1): 49-69.
[24] KAPUR Deepak, SAXENA Tushar, YANG Lu. Algebraic and geometric reasoning using Dixon resultants[C]. Proceedings of the international symposium on Symbolic and algebraic computation, 1994: 99–107.
[25] TROTT Michael. The mathematica guidebook for symbolics
[M]. Springer New York, 2006: 28.
[26] MACAULAY F. S., BY Introduction. The Algebraic Theory of Modular Systems[M]. 19. Cambridge University Press, 1994.
[27] CANNY John, EMIRIS Ioannis. An efficient algorithm for the sparse mixed resultant[M]. Springer Berlin Heidelberg, 1993: 89-104.
[28] VYHLíDAL Tomáš, ZíTEK Pavel: QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples, Vyhlídal T, Lafay J-F, Sipahi R, editor, Delay Systems: From Theory to Numerics and Applications, Cham: Springer International Publishing, 2014: 299-312.