负刚度时滞反馈控制动力吸振器的等峰优化

代晗; 赵艳影

doi:10.6052/0459-1879-21-074

负刚度时滞反馈控制动力吸振器的等峰优化

doi: 10.6052/0459-1879-21-074

代晗,
赵艳影^2), ,

南昌航空大学飞行器工程学院, 南昌 330063

基金项目: 1)国家自然科学基金(12072140);江西省自然科学基金(20202ACBL201003)

详细信息

作者简介:
2)赵艳影, 教授, 主要研究方向: 结构振动与控制. E-mail: yanyingzhao@nchu.edu.cn

通讯作者:
赵艳影

中图分类号: O328,TH213.3
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- 被引次数: 0
出版历程
- 收稿日期: 2021-02-10
- 刊出日期: 2021-06-01

EQUAL-PEAK OPTIMIZATION OF DYNAMIC VIBRATION ABSORBER WITH NEGATIVE STIFFNESS AND DELAY FEEDBACK CONTROL

Dai Han,
Zhao Yanying^{2)
, ,}

Department of Aircraft Engineering, Nanchang Hangkong University, Nanchang 330063, China

摘要

摘要: 相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值.
- 负刚度 /
- 等峰优化 /
- 时滞反馈控制 /
- 动力吸振器 /
- 频带宽度
Abstract: Compared with the traditional dynamic vibration absorber, negative stiffness dynamic vibration absorber has better damping capacity and wider effective damping frequency bandwidth. The time-delay feedback control is coupled into negative stiffness dynamic vibration absorber system to further reduce the amplitude of the resonant peak and increase the bandwidth of the effective damping frequency. In the present paper, the time-delay feedback control dynamic vibration absorber system with negative stiffness is designed by equal-peak optimization. The optimal design criteria are as follows: the peak values of the first and the second resonance peaks are equal; two objectives are considered at the same time, one is to optimize the maximum resonance peak amplitude to be less than the anti-resonance peak amplitude of the passive negative stiffness absorber system, and the other is to optimize the difference between the resonance peak and the anti-resonance peak to be less than the passive absorber system. Then, the equal-peak optimum design of the control system is carried out by designing and adjusting the negative stiffness coefficient, the damper coefficient of vibration absorber and the time-delay feedback control coefficient. Finally, the effect of structural parameters on effective damping frequency bandwidth is analyzed under the condition of reducing amplitude of resonant peak. A set of structural parameters are selected and compared with two typical models based on the results of equal-peak optimization. In order to quantitatively compare the reduction effect of different models, the amplitude reduction percentage is defined. It is found that the percentage amplitude reduction is over 40% in the effective damping frequency band. The results show that the percentage reduction of the resonance peak amplitude also approximates to 40% by optimizing the structural parameters and adjusting the gain coefficient and time delay. In addition, the amplitude-frequency response curve has wider effective damping frequency bandwidth and a lower difference between the amplitude of the resonance peak and the amplitude of the anti-resonance peak by adjusting gain coefficient and time delay.
- negative stiffness /
- equal-peak optimization /
- delayed feedback control /
- dynamic vibration absorber /
- frequency bandwidth

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参考文献(36)

[1]	Frahm H. Device for damping vibrations of bodies. U.S. Patent 0989958. 1909-10-30
[2]	Den Hartog JP. Mechanical Vibrations. New York: McGraw-Hall Book Company, 1947: 112-132
[3]	Ormondroyd J, Den Hartog JP. The theory of dynamic vibration absorber. Journal of Applied Mechanics-Transactions of the ASME, 1928, 50: 9-22
[4]	Brock JE. A note on the damped vibration absorber. Transaction of the American Society of Mechanical Engineers, 1946, 13(4): A-284
[5]	Liu KF, Liu J. The damped dynamic vibration absorbers: Revisited and new result. Journal of Sound and Vibration, 2005, 284(3): 1181-1189
[6]	Asami T, Nishihara O. Closed-form exact solution to $H_{infty }$ optimization of dynamic vibration absorbers (application to different transfer functions and damping systems). Journal of Vibration and Acoustics, 2003, 125(3): 398-405
[7]	Nishihara O, Asami T. Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors). Journal of Vibration and Acoustics, 2002, 124(4): 576-582
[8]	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. 力学学报, 2015, 47(2): 320-327 (Peng Haibo, Shen Yongiun, Yang Shaopu. Parameters optimization of a new type of dynamic vibration absorber with negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 320-327 (in Chinese))
[9]	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. 力学学报, 2019, 51(3): 894-903 (Xing Zhaoyang, Shen Yongjun, Xing Haijun, et al. Parameters optimization of a dynamic vibration absorber with amplifying mechanism and negative stiffness. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 894-903 (in Chinese))
[10]	Benacchio S, Malher A, Boisson J, et al. Design of a magnetic vibration absorber with tunable stiffnesses. Nonlinear Dynamics, 2016, 85(2): 893-911
[11]	刘刚, 郑大胜, 丁志雨等. 变质量-负刚度动力吸振器试验研究. 中国机械工程, 2018, 29(5): 538-543 (Liu Gang, Zheng Dasheng, Ding Zhiyu, et al. Experimental study on variable ma- ss negative stiffness dynamic vibration absorbers. China Mechanical Engineering, 2018, 29(5): 538-543 (in Chinese))
[12]	李强, 董光旭, 张希农等. 新型可调动力吸振器设计及参数优化. 航空学报, 2018, 39(6): 128-140 (Li Qiang, Dong Guangxu, Zhang Xinong, et al. Design and parameter optimization of a new tunable dynamic vibration absorber. Acta Aeronautica et Astronautica Sinica, 2018, 39(6): 128-140 (in Chinese))
[13]	胡方圆, 刘清华, 曹军义等. 负刚度非线性系统的回复力曲面参数辨识方法. 西安交通大学学报, 2021, 55(4): 95-106 (Hu Fangyuan, Liu Qinghua, Cao Junyi, et al. Restoring force surface-based parameter identification method for negative stiffness nonlinear system. Journal of Xi'an Jiaotong University, 2021, 55(4): 95-106 (in Chinese))
[14]	郎君, 申永军, 杨绍普. 一种半主动动力吸振器参数优化及性能比较. 振动与冲击, 2019, 38(17): 172-177 (Lang Jun, Shen Yongjun, Yang Shaopu. Parametric optimization and performance comparison for 2 semi-active voigt DVAs. Journal of Vibration and Shock, 2019, 38(17): 172-177 (in Chinese))
[15]	张婉洁, 牛江川, 申永军等. 一类阻尼控制半主动隔振系统的解析研究. 力学学报, 2020, 52(6): 1743-1754 (Zhang Wanjie, Niu Jiangchuan, Shen Yongjun, et al. Dynamical analysis on a kind of semi-active vibration isolation systems with damping control. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1743-1754 (in Chinese))
[16]	李锁斌, 魏儒义, 周安安等. 超结构夹芯板及其低宽频振动带隙机理. 西安交通大学学报, 2021, 55(4): 77-85 (Li Suobin, Wei Ruyi, Zhou An'an, et al. Sandwich type metamaterial plate and its mechanism of low-frequency broad vibration band gap. Journal of Xi'an Jiaotong University, 2021, 55(4): 77-85 (in Chinese))
[17]	Li ZY, Sheng MP, Wang MQ, et al. Stacked dielectric elastomer actuator (SDEA): Casting process, modeling and active vibration isolation. Smart Materials and Structures, 2018, 27: 7
[18]	Gripp JAB, Góes LCS, Heuss O, et al. An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure. Smart Material Structures, 2015, 24: 125017
[19]	Sun SS, Yang J, Li WH, et al. Development of an MRE adaptive tuned vibration absorber with self-sensing capability. Smart Materials and Structures, 2015, 24(9): 095012
[20]	Kumbhar SB, Chavan SP, Gawade SS. Adaptive tuned vibration absorber based on magnetorheological elastomer-shape memory alloy composite. Mechanical Systems and Signal Processing, 2018, 100(1): 208-223
[21]	Thenozhi S, Yu W. Stability analysis of active vibration control of building structures using PD/PID control. Engineering Structures, 2014, 81(15): 208-218
[22]	Shan JJ, Liu HT, Sun D. Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF). Mechatronics, 2005, 15(4): 487-503
[23]	Orlando C, Alaimo A. A robust active control system for shimmy damping in the presence of free play and uncertainties. Mechanical Systems and Signal Processing, 2017, 84: 551-569
[24]	Lin TC. Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(12): 4084-4099
[25]	McDaid AJ, Mace BR. A robust adaptive tuned vibration absorber using semi-passive shunt electronics. IEEE Transactions on Industrial Electronics, 2016, 63(8): 5069-5077
[26]	Thenozhi S, Wen Y. Sliding mode control of wind-induced vibrations using fuzzy sliding surface and gain adaptation. International Journal of Systems Science, 2016, 47: 1258
[27]	Olgac N, Holm-Hansen BT. A novel active vibration absorption technique: delayed resonator. Journal of Sound and Vibration, 1994, 176(1): 93-104
[28]	Sipahi R, Olgac N, Breda D. A stability study on first-order neutral systems with three rationally independent time delays. International Journal of Systems Science, 2010, 41(12): 1445-1455
[29]	Zhao YY. Vibration suppression of a saturation control system using delayed feedback control. Applied Mechanics and Materials, 2012, 226-228: 82-86
[30]	Zhao YY, Xu J. Effects of delayed feedback control on nonlinear vibration absorber system. Journal of Sound and Vibration, 2007, 308(1-2): 212-230
[31]	Wang F, Sun XT, Meng H, et al. Time-delayed feedback control design and its application for vibration absorption. IEEE Transact- ions on Industrial Electronics, 2020, PP(99): 1-1
[32]	Wang F, Xu J. Parameter design for a vibration absorber with time-delayed feedback control. Acta Mechanica Sinica, 2019, 35(3): 624-640
[33]	Sun XT, Xu J, Wang F, et al. Design and experiment of nonlinear absorber for equal-peak and de-nonlinearity. Journal of Sound and Vibration, 2019, 449: 274-299
[34]	Meng H, Sun XT, Xu J, et al. The generalization of equal-peak method for delay-coupled nonlinear system. Physica D: Nonlinear Phenomena, 2020, 403: 132340
[35]	吴旭东, 张茗海, 左曙光等. 振子质量非均布的有限结构梁减振频带优化. 振动工程学报, 2019, 32(6): 935-942 (Wu Xudong, Zhang Minghai, Zuo Shuguang, et al. Optimization of damping frequency band in finite structure beam with uneven mass distribution of oscillator. Journal of Vibration Engineering, 2019, 32(6): 935-942 (in Chinese))
[36]	Vyhlídal T, Lafay JF, Sipahi R. Delay Systems: From Theory to Numerics and Applications. Cham: Springer International Publishing, 2014: 299-312