| ANALYSIS OF BREATHER STATE IN THIN BAR BY USING COLLECTIVE COORDINATE |
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| 作者姓名： | 赵广慧 张年梅 杨桂通 |
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| 作者单位： | [1]School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, P. R. China [2]Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China |
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| 基金项目： | 国家自然科学基金;山西省自然科学基金 |
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| 摘 要： | Considering Peierls-Nabarro (P-N) force and viscous effect of material, the dynamic behavior of one-dimensional infinite metallic thin bar subjected to axially periodic load is investigated. Governing equation, which is sine-Gordon type equation, is derived. By means of collective-coordinates, the partial equation can be reduced to ordinary differential dynamical system to describe motion of breather. Nonlinear dynamic analysis shows that the amplitude and frequency of P-N force would influence positions of hyperbolic saddle points and change subharmonic bifurcation point, while the path to chaos through odd subharmonic bifurcations remains. Several examples are taken to indicate the effects of amplitude and period of P-N force on the dynamical response of the bar. The simulation states that the area of chaos is half-infinite. This area increases along with enhancement of the amplitude of P-N force. And the frequency of P-N force has similar influence on the system.
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| 关 键 词： | 通气孔 应力波 坐标 分谐波 |
| 收稿时间： | 2005-07-20 |
| 修稿时间： | 2006-07-19 |
Analysis of breather state in thin bar by using collective coordinate |
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| Guang-hui Zhao Doctor,Nian-mei Zhang,Gui-tong Yang.ANALYSIS OF BREATHER STATE IN THIN BAR BY USING COLLECTIVE COORDINATE[J].Applied Mathematics and Mechanics(English Edition),2006,27(12):1597-1605. |
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| Authors: | Guang-hui Zhao Doctor Nian-mei Zhang Gui-tong Yang |
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| Institution: | 1. School of Mechanical Engineering, Southwest Petroleum University, Chengdu,610500, P. R. China
2. Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan,030024, P. R. China |
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| Abstract: | Considering Peierls-Nabarro (P-N) force and viscous effect of material, the dynamic behavior of one-dimensional infinite metallic thin bar subjected to axially periodic load is investigated. Governing equation, which is sine-Gordon type equation, is derived. By means of collective-coordinates, the partial equation can be reduced to ordinary differential dynamical system to describe motion of breather. Nonlinear dynamic analysis shows that the amplitude and frequency of P-N force would influence positions of hyperbolic saddle points and change subharmonic bifurcation point, while the path to chaos through odd subharmonic bifurcations remains. Several examples are taken to indicate the effects of amplitude and period of P-N force on the dynamical response of the bar. The simulation states that the area of chaos is half-infinite. This area increases along with enhancement of the amplitude of P-N force. And the frequency of P-N force has similar influence on the system. |
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| Keywords: | collective coordinate sine-Gordon equation Melnikov method subharmonic bifurcation chaos |
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