Analysis of Breather State in Thin Bar by Using Collective Coordinate
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摘要: 研究了计入Peierls-Nabarro(P-N)力和材料粘性效应的一维无限长金属杆在简谐外力扰动下的动力响应，导出了类sine-Gordon 型的运动方程．在集结坐标(collective coordinate）下原控制方程可以用常微分动力系统描述，研究系统中呼吸子的运动．根据非线性动力学方法分析，P-N力的幅值和频率的变化将改变双曲鞍点的位置，并改变系统次谐分叉的阈值，但不改变由奇阶次谐分叉通向混沌的路径．通过实例给出了P-N力幅值和P-N力频率对细杆动力响应的详细影响过程，可见混沌发生的区域是一个半无限区域，并随着P-N力的增大而增大．P-N力的频率对系统有类似的影响．
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关键词:
- 集结坐标 /
- sine-Gordon方程 /
- Melnikov方法 /
- 亚谐分叉 /
- 混沌
Abstract: Considering Peierls-Nabarro (P-N) force and visco us effect of material, the dynamic behavior of one-dimensional infinite metallic thin barsubjected to axially periodic load was investigated. Governing equation, which was sine-Gordon type equation, was derived. By means of collective-coordinates, the partialequation could be reduced into ordinary differential dynamical system to describemotion of breather. Nonlinear dynamic analysis shows that the amplitude and frequency of P-N force would influence positions of hyperbolic saddlepoints and change subharmonic bifurcation point, while the path to chaos through oddsubhar monic bifurcations remains. Several examples were taken to indicate the effects of amplitude and perio d of P-N force o n the dy namical re sponse o f the bar. The simulatio n states that the area of chaos is half-infinite. This are a incre ases along with enhancement of the amplitude of P-N force. And the frequency of P-N force has similar influence on the system.-
Key words:
- collective coordinate /
- sine-Grdon equation /
- Melnikov method /
- subharmonic bifurcation /
- chaos
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