一类刚弹混合碰撞系统的动力学分析
Analysis on a Kind of Rigid-Elastic Hybrid Collision System
DOI: 10.12677/DSC.2018.72014, PDF,    科研立项经费支持
作者: 皇甫玉高, 杨国英：河南理工大学数学与信息科学学院，河南 焦作
关键词: 分段线性碰撞系统；周期碰撞；数值仿真；Piecewise Linear Collision System； Periodic Collision； Numerical Simulation
摘要: 为了研究动力系统中同时含有刚性碰撞过程和弹性碰撞过程时的系统特性，本文给出了一类新的既含有刚性碰撞又含有弹性碰撞过程的碰撞振动模型。通过建立全局Poincaré映射的方法解析的分析了此碰撞振动系统的一周期一碰及一周期n碰的周期运动条件。数值仿真模拟了系统的周期碰撞运动现象，并得到了随参数发生变化时，系统出现的分岔现象，且利用数值仿真的方法对系统中的共存吸引子进行了初步研究。
Abstract: In order to study the system characteristics of a dynamic system with both rigid and elastic colli-sions, a new type of collisional vibration model with both rigid and elastic collisions is presented in this paper. A global Poincaré mapping method is used to analyze the conditions of one-collision- one-period and n-collisions-one-period motion vibration system. The numerical simulation simu-lates the system’s periodic collision movement phenomenon, and obtains the bifurcation phe-nomenon that occurs when the parameters change with the system. The numerical simulation method is used to study the coexistence attractors in the system.
文章引用：皇甫玉高, 杨国英. 一类刚弹混合碰撞系统的动力学分析[J]. 动力系统与控制, 2018, 7(2): 124-134. https://doi.org/10.12677/DSC.2018.72014

参考文献

[1] Wiggins, S. (1990) Introduction to Applied Non-linear Dynamical Systems and Chaos. Springer-Verlag, New York.
[2] Guckenheimer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York.
[3] Kuznetsov, Y.A. (1998) Elements of Applied Bifurcation Theory. 2nd Edition, Springer-Verlag, New York.
[4] Hartog, J.P.D. and Mikina, S.J. (1932) Forced Vibrations with Non-Linear Spring Constants. Journal of Applied Mechanics, 58, 157-164.
[5] Shaw, S.W. and Holmes, P.J. (1983) A Periodically Forced Piecewise Linear Oscillator. Journal of Sound and Vibration, 90, 121-155.
[6] Nordmark, A.B. (1991) Non-Periondic Motion Caused by Grazing Incidence in an Impact Oscillator. Journal of Sound and Vibration, 145, 279-297.
[7] Kleczka, M., Kreuzer, E. and Schiehlen, W. (1992) Local and Global Stability of a Piecewise Linear Oscillator. Philosophical Transactions of the Royal Society A, 338, 533-546.
[8] Wiercigroch, M. (2000) Modeling of Dynamical System with Motion Dependent Discontinuities. Chaos, Solitons & Fractals, 11, 2429-2442.
[9] Luo, G.W., Xie, J.H. and Guo, S.H.L. (2001) Periodic Motions and Global Bifurcations of a Two-Degree-of-Freedom System with Plastic Vibro-Impact. Journal of Sound and Vibration, 240, 837-858.
[10] Luo, A.C.J. (2002) An Unsymmetrical Motion in a Horizontal Impact Oscillator. Journal of Vibration and Acoustics, 124, 420-426.
[11] Luo, A.C.J. and Menon, S. (2004) Global Chaos in a Periodically Forced, Linear System with a Dead-Zone Restoring Force. Chaos, Solitons and Fractals, 19, 1189-1199.
[Google Scholar] [CrossRef] 
[12] Luo, A.C.J. (2005) The Mapping Dynamics of Periodic Motions for a Three-Piecewise Linear System under a Periodic Excitation. Journal of Sound and Vibration, 283, 723-748.
[Google Scholar] [CrossRef] 

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