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Nonlinear complex dynamic phenomena of the perturbed metallic bar considering dissipating effect

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Abstract

Considering Peierls-Nabarro effect, one-dimensional finite metallic bar subjected with periodic field was researched under Neumann boundary condition. Dynamics of this system was described with displacement by perturbed sine-Gordon type equation. Finite difference scheme with fourth-order central differences in space and second-order central differences in time was used to simulate dynamic responses of this system. For the metallic bar with specified sizes and physical features, effect of amplitude of external driving on dynamic behavior of the bar was investigated under initial “breather” condition. Four kinds of typical dynamic behaviors are shown: x-independent simple harmonic motion; harmonic motion with single wave; quasi-periodic motion with single wave; temporal chaotic motion with single spatial mode. Poincaré map and power spectrum are used to determine dynamic features.

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Authors and Affiliations

  1. Institute of Applied Mechanics, Taiyuan University of Technology, 030024, Taiyuan, P.R.China

    Zhao Guang-hui, Zhang Nian-mei & Yang Gui-tong

Authors
  1. Zhao Guang-hui
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  2. Zhang Nian-mei
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  3. Yang Gui-tong
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Additional information

Contributed by YANG Gui-tong, Original Member of Editorial Committee, AMM

Foundation items: the National Natural Science Foundation of China (10172063); Youth Science Foundation of Shanxi Province, China (20011004)

Biographies: ZHAO Guang-hui, Lecturer, Doctor, E-mail: wy_zgh@yahoo.com.cn

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Zhao, Gh., Zhang, Nm. & Yang, Gt. Nonlinear complex dynamic phenomena of the perturbed metallic bar considering dissipating effect. Appl Math Mech 26, 142–149 (2005). https://doi.org/10.1007/BF02438235

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  • DOI: https://doi.org/10.1007/BF02438235

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2000 Mathematics Subject Classification

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