Analysis of Breather State in Thin Bar by Using Collective Coordinate

ZHAO Guang-hui; ZHANG Nian-mei; YANG Gui-tong

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ZHAO Guang-hui, ZHANG Nian-mei, YANG Gui-tong. Analysis of Breather State in Thin Bar by Using Collective Coordinate[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1397-1404.

Citation:

ZHAO Guang-hui, ZHANG Nian-mei, YANG Gui-tong. Analysis of Breather State in Thin Bar by Using Collective Coordinate[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1397-1404.

Citation:

ZHAO Guang-hui, ZHANG Nian-mei, YANG Gui-tong. Analysis of Breather State in Thin Bar by Using Collective Coordinate[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1397-1404.

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Analysis of Breather State in Thin Bar by Using Collective Coordinate

1.
Mechatronic Engineering College, Southwest Petroleum University, Chengdu 610500, P. R. China;

Received Date: 2005-05-20
Rev Recd Date: 2006-07-19
Publish Date: 2006-12-15

Abstract

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.
- collective coordinate,
- sine-Grdon equation,
- Melnikov method,
- subharmonic bifurcation,
- chaos

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References(11)

References

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