冲击渐进振动系统的双参数分岔分析

吕小红1, 2 罗冠炜2

振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 50-56.

PDF(1288 KB)
PDF(1288 KB)
振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 50-56.
论文

冲击渐进振动系统的双参数分岔分析

  • 吕小红1, 2   罗冠炜2
作者信息 +

Two-parameter bifurcation analysis for an impact progressive vibration system

  • L Xiaohong1,2, LUO Guanwei2
Author information +
文章历史 +

摘要

建立了冲击渐进振动系统的力学模型。分析了激振器和缓冲垫发生碰撞的类型,以及滑块渐进运动的条件。给出了系统可能呈现的四种运动状态的判断条件和运动微分方程。通过二维参数分岔分析得到在( , l) -参数平面内各点处,系统呈现的周期振动的类型。详细分析了1/1和2/1基本碰撞运动的分岔特点,以及系统参数、冲击速度和滑块渐进率之间的关联关系。1/1基本碰撞运动经周期倍化分岔产生2/2周期振动,经虚擦边分岔或多重滑移分岔产生2/1基本碰撞运动。2/1基本碰撞运动经实擦边分岔,虚擦边分岔或多重滑移分岔产生3/1基本碰撞运动。由于p/1(p=1, 2)基本碰撞运动的虚擦边分岔,使得p/1基本碰撞运动在向稳定的(p+1)/1基本碰撞运动转迁的过程中出现一个中间过渡区域。此外,在一定参数条件下,系统呈现1/1基本碰撞运动的概周期运动和周期泡现象。

Abstract

The mechanical model of an impact progressive vibration system was established. Impact types between a vibration exciter and a cushion,and progressive motion conditions of a slider were analyzed. Judgment conditions and dynamic equations for 4 possible motion states of the system were derived. Based on bifurcation analysis in a 2-D parametric plane,periodic vibration types of the system were obtained at all points in the parametric plane of (ω,l). The bifurcation characteristics of the fundamental impact motions of 1/1 and 2/1 were analyzed in detail. The relations among system parameters,impact velocity and slider’s progressive motion rate were studied. It was shown that the fundamental impact motion of 1/1 produces the periodic vibration of 2/2 through period-doubling bifurcation,and it produces the fundamental impact motion of 2/1 through virtual erasure bifurcation or multi-slip one; the fundamental impact motion of 2/1 produces the fundamental impact motion of 3/1 through real erasure bifurcation,virtual erasure one or multi-slip one; due to virtual erasure bifurcation of the fundamental impact motion of p/1(p=1,2),an intermediate transition region appears in the transition process from the fundamental impact motion of p/1 to the stable fundamental impact motion of (p+1)/1; the system exhibits a quasi-periodic motion and a periodic bubble phenomenon of the fundamental impact motion of 1/1 under certain parametric conditions.

关键词

非光滑系统 / 冲击振动 / 渐进 / 基本碰撞运动 / 分岔

Key words

non-smooth system / vibro-impact / progression / fundamental impact motion / bifurcation

引用本文

导出引用
吕小红1, 2 罗冠炜2. 冲击渐进振动系统的双参数分岔分析[J]. 振动与冲击, 2019, 38(7): 50-56
L Xiaohong1,2, LUO Guanwei2. Two-parameter bifurcation analysis for an impact progressive vibration system[J]. Journal of Vibration and Shock, 2019, 38(7): 50-56

参考文献

[1] Wen GL, Xie JH, Xu DL. Onset of degenerate Hopf bifurcation of a vibro-impact oscillator [J]. Journal of Applied Mechanics –Transactions of the ASME, 2004, 71(4): 579―581.
[2] 张永祥, 孔贵芹, 俞建宁. 振动筛系统的Hopf-Hopf- Flip分岔与混沌演化[J]. 工程力学, 2009, 26(1): 233―237.
Zhang Yong-xiang,  Kong Gui-qin, Yu Jian-ning. Hopf- hopf-flip bifurcation and routes to chaos of a shaker system [J]. Engineering Mechanics, 2009, 26(1): 233―237.
[3] 乐源. 一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学[J]. 力学学报, 2016, 48(1): 163―172.
Yue Yuan. Local dynamical behavior of two-parameter family near the neimark-sacker-pitchfork bifurcation point in a vibro-impact system [J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 163―172.
[4] 李群宏, 陆启韶. 一类双自由度碰振系统运动分析[J]. 力学学报, 2001, 33(6): 776―786.
Li Qunhong, Lu Qishao. Analysis to motions of a two-degree-of- freedom vibro-impact system [J]. Acta Mechanica Sinca, 2001, 33(6): 776―786.
[5] 朱喜锋, 罗冠炜. 两自由度含间隙弹性碰撞系统的颤碰运动分析[J]. 振动与冲击, 2015, 34(15): 195―200.
Zhu Xifeng, Luo Guanwei. Chattering-impact motion of 2-DOF system with clearance and soft impacts [J]. Journal of Vibration and Shock, 2015, 34(15): 195―200.
[6] 张思进, 周利彪, 陆启韶. 线性碰振系统周期解擦边分岔的一类映射分析方法[J]. 力学学报,2007, 37(1): 132―136.
Zhang Sijin, Zhou Libiao, Lu Qishao. A map method for grazing bifurcatin in linear vibro-impact system [J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 13―136.
[7] Chillingworth D R J. Dynamics of an impact oscillator near a degenerate graze [J]. Nonlinearity, 2010, 23: 2723―2748.
[8] Humphries N, Piiroinen P T. A discontinuity-geometry view of the relationship between saddle–node and grazing bifurcations [J]. Physica D, 2012, 241(22): 1911―1918.
[9] Liu Yongbao, Wang Qiang, Xu Huidong. Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance [J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 48(7): 1―17.
[10] 冯进钤, 徐伟. 碰撞振动系统中周期轨道擦边诱导的混沌激变[J]. 力学学报, 2013, 45(1): 30―36.
Feng Jinqian, Xu Wei. grazing-induced chaostic crisis for periodic orbits in vibro-impact systems [J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 30―36.
[11] Feng jinqian. Analysis of chaotic saddles in a nonlinear vibro-impact system [J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 48(7): 39―50.
[12] Peterka F, Tondl A. Phenomena of subharmonic motions of oscillator with soft impacts [J]. Chaos, Solitons and Fractals, 2004, 19: 1283―1290.
[13] Peterka F, Blazejczyk-Okolewska B. Some Aspects of the dynamical behavior of the impact damper [J]. Journal of Vibration and Control, 2005, 11: 459―479.
[14] Chávez J P, Pavlovskaia E, Wiercigroch M. Bifurcation analysis of a piecewise-linear impact oscillator with drift [J]. Nonlinear Dynamics, 2014, 77(1-2): 213―227.
[15] Pavlovskaia E, Hendry D C, Wiercigroch M. Modelling of high frequency vibro-impact drilling [J]. International Journal of Mechanical Sciences, 2015, 91(2): 110―119.
[16] Luo GW, Zhu XF, Shi YQ. Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop: Diversity and evolution of periodic-impact motions [J]. Journal of Sound and Vibration, 2015, 334(6): 338―362.
[17] Wagg D J. Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator [J]. Chaos, Solitons and Fractals, 2004, 22(3): 541―548.

PDF(1288 KB)

Accesses

Citation

Detail

段落导航
相关文章

/