Resonance, Bifurcations and Chaos of Periodic Motion of a Vibro-Impact System

机译：振动冲击系统的周期运动的共振，分岔和混沌

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A two-degree-of-freedom vibro-impact system is considered in this paper. The dynamical model and Poincare map are established. When pairs of complex conjugate eigenvalues of the Jacobi matrix cross the unit circle and satisfy the conditions of resonance cases, some dynamical behaviors of vibro-impact system are investigated by theoretical analysis. Furthermore torus oscillation, phase locking and evolutive route to chaos via torus bifurcations are discussed by numerical simulations.

机译：本文考虑了一种两自由度的振动系统。建立动力学模型和庞加莱图。当雅可比矩阵的复共轭共轭特征值对穿过单位圆并满足共振条件时，通过理论分析研究了振动冲击系统的一些动力学行为。此外，通过数值模拟讨论了圆环振荡，锁相和通过圆环分叉形成混沌的演化路线。

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来源
《International Conference on Mechanical Engineering and Mechanics vol.1; 20051026-28; Nanjing(CN)》|2005年|P.721-725|共5页
会议地点 Nanjing(CN)
作者
Wangcai DING; Mei LIN; Jianhua XIE;
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作者单位

School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类机械设计、计算与制图;
关键词
vibro-impact; poincare map; resonance; bifurcation; chaos;

机译：振动冲击;庞加莱图;共振;分叉;混沌;

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2. Periodic motions and bifurcations of a vibro-impact system [J] . Guanwei Luo, Jianhua Xie, Xifeng Zhu, Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2008,第5期

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3. Periodic motions and global bifurcations of a two-degree-of-freedom system with plastic vibro-impact [J] . Luo GW., Guo SHL., Xie JH. Journal of Sound and Vibration . 2001,第5期

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5. Bifurcation and chaos of nonlinear vibro-impact systems. [D] . Guo, Yu. 2013

机译：非线性振动冲击系统的分叉和混沌。
6. Bifurcations and chaos in a predator-prey system with the Allee effect. [O] . Andrew Morozov, Sergei Petrovskii, Bai-Lian Li 2009

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7. On bifurcations and stability of resonance periodic motions of hamiltonian systems with one degree of freedom caused by degeneration of the hamiltonian [O] . O. V. Kholostova 2006

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8. Dynamics of Coupled Planar Rigid Bodies. Part 2. Bifurcations, Periodic Solutions, and Chaos. [R] . Oh, Y., Eenath, N., Krishnaprasad, P. S., 1988

机译：耦合平面刚体的动力学。第2部分。分叉，周期解和混沌。

Resonance, Bifurcations and Chaos of Periodic Motion of a Vibro-Impact System

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