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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Bishop A R, Flesch R, Forest M G,et al. Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system[J].SIAM J Mathematical Analysis 199021(6):1511–1536.
Bishop A R, Fesser K, Lomdahl P S. Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system[J].Physica D, 1983,7(2):259–279.
Bishop A R, Forest M G, Mclaughlin D W,et al. A quasi-periodic route to chaos in a near-integrable PDE[J].Physica D, 1986,23(2):293–328.
Eilbeck J C, Lomdahl P S, Newell A C. Chaos in the inhomogeneouslydriven sine-Gordon equation [J].Physics Letters A, 1981,87(1):1–4.
Zhang Nianmei, Yang Guitong. Chaotic belt phenomena in nonlinear elastic beam[J].Applied Mathematics and Mechanics (English Edition), 2003,24(5):509–513.
Shu X F, Yang G T. The influence of material properties on dynamic behavior of structures[A]. in: Senoo M (ed.).Proceedings of IMMM’97[C]. Mie University Press, Kamihama, 1997, 279–284.
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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