新型欧拉屈曲梁非线性动力吸振器的实现及抑振特性研究

PDF(2579 KB)

振动与冲击 ›› 2016, Vol. 35 ›› Issue (11) : 155-160.

论文

刘海平，杨建中，罗文波，钱志英

作者信息 +

Developing the structure and analyzing the effectiveness of a novel Euler buckled beam nonlinear vibration absorber

Liu Haiping, Yang Jianzhong, Luo Wenbo, Qian Zhiying

Author information +

文章历史 +

摘要

将欧拉屈曲梁和线性弹簧并联使用，构建非线性动力吸振器。建立了安装欧拉屈曲梁非线性动力吸振器的系统动力学模型。利用谐波平衡法推导了主从振系的频响方程组。利用四阶龙格—库塔法对比计算了在瞬态激励和多频稳态激励条件下，未安装吸振器、安装线性和非线性吸振器时主振系在时间域和频率域的响应特性。在此基础上，开展欧拉屈曲梁的初始挠度、初始倾角和阻尼系数对其振动抑制性能的影响分析。结果表明：所提欧拉屈曲梁设计参数成功构建了改进的本质非线性动力吸振器；与安装线性吸振器前后的主振系响应相比，对主振系的抑振效果明显；欧拉屈曲梁初始挠度和阻尼系数存在最优值；初始倾角增大可增强非线性动力吸振器的振动抑制能力。

Abstract

Combining parallel Euler buckled beam with a linear positive stiffness spring, a new novel improved nonlinear vibration absorber was provided and designed. According to the novel structure, a systematic dynamic model with strong nonlinear characteristic of the nonlinear vibration absorber was proposed. Based on the nonlinear dynamic equations, frequency response expressions were derived by using harmonic balance method. Meanwhile, under these conditions of transient input and multi-frequency stability input, the systematic dynamic equations without absorber, with linear and nonlinear absorber, respectively, were solved by using four-order Runge-Kutta method in time-domain and frequency-domain. In addition, the influences of initial imperfection, oblique angle and damping coefficient of Euler buckled beam on the vibration suppression performance were studied. The calculating results show that a typical improved essentially nonlinear dynamic absorber was constructed successfully based on the provided designing parameters of Euler buckled beam. Compared with the vibration responses of the main mass without and with absorber, it can be concluded that the nonlinear absorber has better attenuation performance. The initial imperfection and damping coefficient of Euler buckled beam exist optimized value, and with the increase of the oblique angle, the vibration control characteristic of the nonlinear vibration absorber has been improved.

导出引用

刘海平，杨建中，罗文波，钱志英. 新型欧拉屈曲梁非线性动力吸振器的实现及抑振特性研究[J]. 振动与冲击, 2016, 35(11): 155-160

Liu Haiping, Yang Jianzhong, Luo Wenbo, Qian Zhiying. Developing the structure and analyzing the effectiveness of a novel Euler buckled beam nonlinear vibration absorber[J]. Journal of Vibration and Shock, 2016, 35(11): 155-160

参考文献

[1] Frahm H. Device for damping vibration of bodies[P]. US Patent, 1909: 989958.
[2] Roberson R E. Synthesis of a nonlinear dynamic vibration absorber[J]. Journal of the Franklin Institute, 1952, 254(3): 205-220.
[3] Oueini S S, Chin C M, Nayfeh A H. Dynamics of a cubic nonlinear vibration absorber[J]. Nonlinear Dynamics, 1999, 20(3): 283-295.
[4] Pun D, Liu Y B. On the design of the piecewise linear vibration absorber[J]. Nonlinear Dynamics, 2000, 22(4): 393-413.
[5] Walsh P L, Lamancusa J S. A variable stiffness vibration absorber for minimization of transient vibrations[J]. Journal of Sound and Vibration, 1992, 158(2): 195-211.
[6] Starosvetsky Y, Gendelman O V. Vibration absorption in systems with a nonlinear energy sink: nonlinear damping[J]. Journal of Sound and Vibration, 2009, 324(3-5): 916-939.
[7] Zhu S J, Zheng Y F, Fu Y M. Analysis of nonlinear dynamics of a two-degree-of-freedom vibration system with nonlinear damping and nonlinear spring[J]. Journal of Sound and Vibration, 2004, 271(1-2): 1-11.
[8] 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[J]. 振动与冲击, 2011， 30（6）: 218-222.
Lou J J, Tang S M, Zhu S J, Zhao C S. Parametric range of improved essentially nonlinear absorber on broad frequency band[J]. Journal of Vibration and Shock, 2011, 30(6): 2108-222.
[9] 赵艳影, 徐鉴. 时滞非线性动力吸振器的减振机理[J]. 力学学报, 2008, 40(1): 98-105.
Zhao Y Y, Xu J. Mechanical analysis of delayed nonlinear vibration absorber[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(1): 98-105.
[10] 唐斯密, 朱石坚, 楼京俊. 非线性吸振器刚度调整策略研究[J]. 武汉理工大学学报, 2011, 35（1）: 163-171.
Tang S M, Zhu S J, Lou J J. Study on the tactic of adjusting stiffness of the nonlinear dynamic vibration absorber[J]. Journal of Wuhan University of Technology, 2011, 35（1）: 163-171.
[11] 刘兴天, 黄修长, 张志谊, 华宏星. 激励幅值及载荷对准零刚度隔振器特性的研究[J]. 机械工程学报, 2013, 49（6）: 89-94.
Liu X T, Huang X C, Zhang Z Y, Hua H X. Influence of excitation amplitude and load on the characteristics of quasi-zero stiffness isolator[J]. Journal of Mechanical Engineering, 2013, 49（6）: 89-94.
[12] 张建卓, 李旦, 董申, 陈明君. 欧拉压杆在超低频垂向隔振系统中的应用研究[J]. 机械强度, 2004, 26(3): 237-241.
Zhang J Z, Li D, Dong S, Chen M J. Study on Euler column spring used in ultra-low frequency vertical vibration isolation system[J]. Journal of Mechanical Strength, 2004, 26(3): 237-241.
[13] Winterflood J, Blair D G, Slagmolen B. High performance vibration isolation using springs in Euler column buckling mode[J] Physics Letters A, 2002, 300: 122-130.
[14] 殷小涛, 孟再强, 刘兴星, 肖心想, 李鸿光. 非规则弹性片高静低动的隔振特性[J]. 噪声与振动控制, 2013, 33（6）: 45-48.
Yin X T, Meng Z Q, Liu X X, Xiao X X, Li H G. High static stiffness and low dynamic stiffness isolation characteristics of irregular elastic sheets[J]. Sound and Vibration Control, 2013, 33（6）: 45-48.
[15] D. Michael McFarland, Lawrence A. Bergman, Alexander F. Vakakis. Experimental study of non-linear energy pumping occurring at a single fast frequency[J], International Journal of Non-linear Mechanics, 40, 2005, pp:891-899.