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Research Papers

Global Behavior of a Vibro-Impact System With Multiple Nonsmooth Mechanical Factors

[+] Author and Article Information
Guofang Li

School of Mechatronic Engineering,
Lanzhou Jiaotong University,
Lanzhou 730070, China
e-mail: 79241683@qq.com

Wangcai Ding

School of Mechatronic Engineering,
Lanzhou Jiaotong University,
Lanzhou 730070, China
e-mail: dingwc@mail.lzjtu.cn

Shaopei Wu

School of Mechatronic Engineering,
Lanzhou Jiaotong University,
Lanzhou 730070, China
e-mail: 351611089@qq.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 7, 2016; final manuscript received June 1, 2017; published online September 7, 2017. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 12(6), 061004 (Sep 07, 2017) (12 pages) Paper No: CND-16-1482; doi: 10.1115/1.4037032 History: Received October 07, 2016; Revised June 01, 2017

A nonlinear mechanical model of a vibro-impact system influenced by double nonsmooth mechanical factors that combine elastic and rigid impact is described. The theoretical solutions to judge the periodic motion stability of the system are presented, and three different “gazing” motions and the corresponding conditions are described. The transition and coupling of periodic motions by the nonsmooth mechanical factors are demonstrated. The formation mechanism of sticking motion, chattering motion, and the periodic cavity by the influence of gazing bifurcation are analyzed. The coexistence of periodic motions and the extreme sensitivity of the initial value within the high frequency region are studied. The distribution of the attractor and the corresponding attracting domain corresponding to different periodic motions are also studied.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic representation of the small stamping mechanical system

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Fig. 2

Schematic diagram of the motion of the impact vibrator

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Fig. 3

Grazing phase diagram of the system

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Fig. 4

The distribution of periodic motion of the system in the parameter domain (ω,g1): (a) periodic motion distribution of the one-sided rigid impact system, (b) periodic motion distribution of the one-sided elastic impact system, and (c) periodic motion distribution of the system with both rigid impact and elastic impact

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Fig. 5

The partial refinement and enlargement of Fig. 4(c): (a) fundamental periodic motion and sticking motion distribution area, (b) periodic motion of inclusions between fundamental periodic motions, and (c) the partial refinement and enlargement of Fig. 5(a), and (d) the partial refinement and enlargement of the periodic cavity

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Fig. 6

Phase plane portraits of the system: (a) grazing motion for case 1 of 1-1-1 motion, ω=0.2962,g1=0.9368, (b) 1-2-1 motion, ω=0.2962,g1=0.9318, and (c) grazing motion for case 2 of 1-2-1 motion, ω=0.2962,g1=0.8917

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Fig. 7

Bifurcation diagram and phase plane portraits of the system: (a) one-parameter bifurcation diagram of traversing the periodic cavity with excitation frequency ω, (b) the partial refinement and enlargement of Fig. 7(a), (c) 1-4-0 grazing motion at ω=0.118337, and (d) 1-4-0 grazing motion at ω=0.121428

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Fig. 8

Periodic motion of the system in the high-frequency region: (a) the periodic motion distribution of the system under initial conditions (1), (b) the periodic motion distribution of the system under initial conditions (2), (c) the periodic motion distribution of the system under conditions (3), and (d) global distribution of periodic motion in the four-dimensional space

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Fig. 9

One-parameter bifurcation diagram under coexistence of periodic motions: (a) one-parameter bifurcation diagram with clearance g1 at ω=2.119 and (b) one-parameter bifurcation diagram with excitation frequency ω at g1=0.0775

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Fig. 10

The attractor and its attracting domain of periodic motion of the system: (a) coexistence of three periods at ω=2.119, g1=0.261, (b) coexistence of three periods at ω=2.119, g1=0.264, (c) coexistence of three periods at ω=2.119, g1=0.268, (d) coexistence of two periods at ω=2.119, g1=0.272, (e) coexistence of two periods at ω=2.119, g1=0.28, (f) coexistence of two periods at ω=2.119, g1=0.283, (g) coexistence of period and chaos at ω=2.119, g1=0.29, (h) coexistence of two periods at ω=2.119, g1=0.2968, (i) coexistence of two periods at ω=2.39, g1=0.0775, (j) coexistence of two periods at ω=2.393, g1=0.0775, (k) coexistence of period and chaos at ω=2.405, g1=0.0775, and (l) coexistence of two periods at ω=2.42, g1=0.0775

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