PERFORMANCE ANALYSIS AND STABILITY STUDY OF DIFFERENT TYPES OF NONLINEAR VIBRATION ABSORBERS WITH COMBINED STIFFNESS OF HORIZONTAL SPRINGS
-
摘要: 动力吸振器作为一种振动控制单元被广泛运用于各种工程场合, 但传统的线性吸振器只能实现窄带振动控制. 文章在线性吸振器的基础上引入对称水平弹簧构建线性刚度与非线性刚度相结合的组合刚度非线性吸振器, 以提升吸振器的吸振性能. 考虑实际工程中可能的安装方式, 分别建立水平弹簧接地安装和不接地安装的组合刚度非线性吸振器模型, 利用谐波平衡法结合弧长延拓法解析求解动力学响应, 并与数值结果相互验证, 证明了求解结果的准确性. 随后分析比较两种组合刚度非线性吸振器与线性吸振器以及非线性能量阱之间的吸振性能, 发现水平弹簧接地安装类型的组合刚度非线性吸振器在保留线性吸振器优势的同时又改善其吸振频带窄的缺点, 且与非线性能量阱相比在主共振频率附近的较宽频内吸振性能更优. 在此基础上, 讨论了水平弹簧参数以及吸振器阻尼对主结构振动幅频响应和稳定性的影响, 最后观察分析主结构幅频响应曲线不稳定区内的复杂动力学行为. 研究结果表明合适的设计参数能够使得主结构振动峰值较低的同时, 频响曲线不稳定运动区域的范围也较小.Abstract: As a kind of vibration control unit, dynamic vibration absorber is widely used in various engineering situations, but the traditional linear vibration absorber can only achieve narrow band vibration control. On the basis of the linear vibration absorber, this paper introduces symmetrical horizontal springs to build a combined stiffness nonlinear vibration absorber with linear stiffness and nonlinear stiffness to improve the vibration absorption performance of the absorber. Considering the possible installation modes in actual projects, the combined stiffness nonlinear vibration absorber models of horizontal spring with grounding and without grounding are established respectively. The dynamic response is solved analytically by the harmonic balance method combined with the arc length continuation method, and the results are mutually verified with the numerical results, which proves the accuracy of the solution results. Then, the vibration absorption performance between two kinds of combined stiffness nonlinear vibration absorbers, the linear vibration absorber, and the nonlinear energy sink is analyzed and compared. It is found that the combined stiffness nonlinear vibration absorbers with horizontal spring grounding installation type not only retain the advantages of the linear vibration absorber, but also improve the shortcomings of its narrow vibration absorption frequency band. In addition, the combined stiffness nonlinear vibration absorber of horizontal springs grounding installation type has better vibration absorption performance in a wider frequency band near the main resonance frequency than the nonlinear energy sink. On this basis, the effects of horizontal spring parameters and absorber damping on the amplitude-frequency response and stability of the main structure are discussed. Finally, the complex dynamic behavior in the unstable region of the amplitude-frequency response curve of the main structure is observed and analyzed. The research results show that the appropriate design parameters can make the vibration peak value of the main structure low, and the unstable movement area of the frequency response curve is also small.
-
Key words:
- combined stiffness /
- nonlinear vibration absorber /
- horizontal spring /
- installation form /
- stability
-
表 1 系统模型参数表
Table 1. Table of model system parameters
Parameter Variable Value main mass m1/ kg 100 main structure stiffness k1/(N·m−1) 4 × 105 main structure damping c1/(N·s·m−1) 253 mass of vibration absorber m2/ kg 10 vertical spring stiffness k2/(N·m−1) 1.47 × 105 vibration absorber damping c2/(N·s·m−1) 50 horizontal spring stiffness k3/(N·m−1) 4.8 × 105 original length l0/m 0.04 precompression length l/m 0.036 external excitation amplitude F0/N 140 -
[1] 吴崇健, 骆东平, 杨叔子等. 离散分布式动力吸振器的设计及在船舶工程中的应用. 振动工程学报, 1999, 12(4): 584-589 (Wu Chongjian, Luo Dongping, Yang Shuzi, et al. Design and application of multiple tuned mass damper for ships. Journal of Vibration Engineering, 1999, 12(4): 584-589 (in Chinese) [2] 蒋圣鹏, 黄子祥, 谢溪凌等. 桨−轴−船艉耦合系统分布式动力吸振器多频优化. 噪声与振动控制, 2021, 41(4): 210-214, 269 (Jiang Shengpeng, Huang Zixiang, Xie Xiling, et al. Multi-frequency optimization of distributed dynamic vibration absorbers for propeller-shaft-stern coupling systems. Noise and Vibration Control, 2021, 41(4): 210-214, 269 (in Chinese) [3] 李剑锋, 龚兴龙, 张先舟等. 主动移频式动力吸振器及其动力特性的研究. 实验力学, 2005, 20(4): 507-514 (Li Jianfeng, Gong Xinglong, Zhang Xianzhou, et al. Study of adaptive tuned vibration absorber and its dynamic properties. Journal of Experimental Mechanics, 2005, 20(4): 507-514 (in Chinese) [4] 傅涛, 上官文斌, 丁乙等. 比例电磁式主动吸振器的设计方法研究. 机械工程学报, 2021, 57(19): 147-154 (Fu Tao, ShangGuan Wenbin, Ding Yi, et al. Design of a proportional electromagnetic active dynamic vibration absorber. Journal of Mechanical Engineering, 2021, 57(19): 147-154 (in Chinese) doi: 10.3901/JME.2021.19.014 [5] Brennan MJ. Some recent developments in adaptive tuned vibration absorbers/neutralizers. Shock and Vibration, 2006, 13: 531-543 [6] Arnold FR. Steady-state behavior of systems provided with nonlinear dynamic vibration. Journal of Applied Mechanics, 1955, 22(4): 487-492 doi: 10.1115/1.4011141 [7] Vakakis AF. Inducing passive nonlinear energy sinks in vibrating systems. ASME Journal of Vibration and Acoustics, 2001, 123(3): 324-332 doi: 10.1115/1.1368883 [8] Gendelman OV, Gorlov D, Manevitch L, et al. Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses. Journal of Sound and Vibration, 2005, 286(1-2): 1-19 doi: 10.1016/j.jsv.2004.09.021 [9] Ding H, Chen LQ. Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dynamics, 2020, 100: 3061-3107 doi: 10.1007/s11071-020-05724-1 [10] 张文勇, 牛牧青, 陈立群. 含串联非线性能量汇的整星系统吸振效果研究. 振动与冲击, 2020, 39(21): 151-155, 172 (Zhang Wenyong, Niu Muqing, Chen Liqun. Vibration absorption effect of whole satellite system with series nonlinear energy sink. Journal of Vibration and Shock, 2020, 39(21): 151-155, 172 (in Chinese) [11] 李晨, 陈国一, 方勃等. 杠杆型并联非线性能量阱的振动控制. 振动与冲击, 2021, 40(15): 54-64 (Li Chen, Chen Guoyi, Fang Bo, et al. Vibration control for lever-type parallel nonlinear energy trap. Journal of Vibration and Shock, 2021, 40(15): 54-64 (in Chinese) [12] 王国旭, 丁虎, 陈立群. 简谐激励下双弹簧非线性能量阱的优化. 动力学与控制学报, 2021, 19(6): 46-51Wang Guoxu, Ding Hu, Chen Liqun. Optimization of a nonlinear energy sink with double spring and harmonic excitation, Journal of Dynamics and Control, 2021, 19(6): 46-51 (in Chinese)) [13] 鲁正, 王自欣, 吕西林. 非线性能量阱技术研究综述. 振动与冲击, 2020, 39(4): 1-16, 26 (Lu Zheng, Wang Zixin, Lü Xilin. A review on nonlinear energy sink technology. Journal of Vibration and Shock, 2020, 39(4): 1-16, 26 (in Chinese) [14] 时成龙, 张纪刚, 程赟. 非线性能量阱减振的研究进展. 地震工程与工程振动, 2021, 41(2): 162-174 (Shi Chenglong, Zhang Jigang, Cheng Yun. Research progress of nonlinear energy sink vibration reduction. Earthquake Engineering and Engineering Vibration, 2021, 41(2): 162-174 (in Chinese) [15] 张运法, 孔宪仁, 岳程斐. 耦合组合刚度非线性能量阱的线性振子动力学分析. 振动与冲击, 2022, 41(13): 103-111, 151 (Zhang Yunfa, Kong Xianren, Yue Chengfei. Dynamic analysis of linear oscillator with coupled combined stiffness NES. Journal of Vibration and Shock, 2022, 41(13): 103-111, 151 (in Chinese) doi: 10.13465/j.cnki.jvs.2022.13.014 [16] 刘海平, 申大山, 王添. 不同类型欧拉屈曲梁非线性吸振器动态特性的影响研究. 振动工程学报, 2022, 35(3): 643-651 (Liu Haiping, Shen Dashan, Wang Tian. Characteristics of different kinds of nonlinear dynamic vibration absorber using Euler-buckled beam. Journal of Vibration Engineering, 2022, 35(3): 643-651 (in Chinese) doi: 10.16385/j.cnki.issn.1004-4523.2022.03.014 [17] 楼京俊, 唐斯密, 朱石坚等. 改进的本质非线性吸振器宽频吸振参数域研究. 振动与冲击, 2011, 30(6): 218-222 (Lou Jingjun, Tang Simi, Zhu Shijian, et al. Parametric range of improved essentially nonlinear absorber on broad frequency band. Journal of Vibration and Shock, 2011, 30(6): 218-222 (in Chinese) [18] Malatkar P, Nayfeh AH. Steady-State dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator. Nonlinear Dynamics, 2006, 47(1-3): 167-179 doi: 10.1007/s11071-006-9066-4 [19] Chang YP, Zhou JX, Wang K, et al. A quasi-zero-stiffness dynamic vibration absorber. Journal of Sound and Vibration, 2021, 494: 115859 [20] Yang K, Zhang YW, Ding H, et al. Nonlinear energy sink for whole-spacecraft vibration reduction. ASME Journal of Vibration and Acoustics, 2017, 139(2): 1-19 [21] Mcfarland DM, Bergman LA, Vakakis AF. Experimental study of non-linear energy pumping occurring at a single fast frequency. International Journal of Non-Linear Mechanics, 2005, 40(6): 891-899 doi: 10.1016/j.ijnonlinmec.2004.11.001 [22] 陆泽琦, 杨铁军, 陈立群等. 非线性动力吸振系统动力学分析和优化. 振动工程学报, 2016, 29(5): 765-771 (Lu Zeqi, Yang Tiejun, Chen Liqun, et al. Dynamical behavior and optimization of a nonlinear vibration absorber. Journal of Vibration Engineering, 2016, 29(5): 765-771 (in Chinese) [23] Carrella A, Brennan MJ, Waters TP. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 2007, 301(3-5): 678-689 doi: 10.1016/j.jsv.2006.10.011 [24] Hao Z, Cao Q, Wiercigroch M. Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dynamics, 2016, 87(2): 987-1014 [25] Gourdon E, Alexander NA, Taylor CA, et al. Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results. Journal of Sound and Vibration, 2007, 300(3-5): 522-551 doi: 10.1016/j.jsv.2006.06.074 [26] Zhao YH, Du JT, Chen YL, et al. Comparison study of the dynamic behavior of a generally restrained beam structure attached with two types of nonlinear vibration absorbers. Journal of Vibration and Control, 2022, doi: 10.1177/10775463221122141 [27] Nayfeh AH, Mook DT. Nonlinear oscillations. Hoboken: John Wiley & Sons, 2008 [28] 刘延柱, 陈立群. 非线性振动. 北京: 高等教育出版社, 2001Liu Yanzhu, Chen Liqun. Nolinear Vibration. Beijing: Higher Education Press, 2001 (in Chinese) [29] Manuel RC, Dinar C. On the arc-length and other quadratic control methods: Established, less known and new implementation procedures. Computers and Structures, 2008, 86: 1353-1368 [30] Rheinboldt WC, Burkardt JV. A locally parameterized continuation process. ACM Transactions on Mathematical Software (TOMS) , 1983, 9(2): 215-235 doi: 10.1145/357456.357460 [31] 吴昊, 李伟固. 非线性拟周期方程的Floquet理论. 中国科学: A辑, 2005, 35(10): 1120-1131 (Wu Hao, Li Weigu. Floquet theory for nonlinear quasiperiodic equations. Chinese Science:Part A, 2005, 35(10): 1120-1131 (in Chinese) [32] Friedmann P, Hammond C, Woo TH. Eifficient numerical treatment of periodic systems with application to stability problems. International Journal for Numerical Methods in Engineering, 1997, 11(7): 11117-11136 [33] Taghipour J, Dardel M. Steady state dynamics and robustness of a harmonically excited essentially nonlinear oscillator coupled with a two-DOF nonlinear energy sink. Mechanical Systems and Signal Processing, 2015, 62-63: 164-182 doi: 10.1016/j.ymssp.2015.03.018 -