Nonlinear Complex Dynamic Phenomena of the Perturbed Metallic Bar Considering Dissipating Effect
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摘要: 研究在周期外载荷作用及Neumann边界条件下，考虑Peierls-Nabarro效应的有限长一维金属杆的运动，以位移表达杆的控制方程，是受扰动的类sine-Gordon方程．利用空间四阶精度，时间二阶精度的有限差分格式模拟系统的动力响应．对于一定特征尺寸及物理性质的金属杆，研究了初始呼吸子及周期载荷幅值对杆动力行为的影响，结果显示了4种典型的动力行为：与空间位置无关的简谐运动、单波的简谐运动、单波的准周期运动和单空间模态的时间混沌运动．通过Poincaré截面和功率谱确定系统的运动特征．
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关键词:
- sine-Gordon系统 /
- Neumann边界条件 /
- 混沌
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.Poincar map and power spectrum are used to determine dynamic features.-
Key words:
- sine-Gordon system /
- Neumann boundary condition /
- chaotic
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[1] 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,1990,21(6):1511—1536. doi: 10.1137/0521083 [2] 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. doi: 10.1016/0167-2789(83)90130-6 [3] 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. doi: 10.1016/0167-2789(86)90137-5 [4] Eilbeck J C, Lomdahl P S,Newell A C.Chaos in the inhomogeneously driven sine-Gordon equation[J].Physics Letters A,1981,87(1): 1—4. doi: 10.1016/0375-9601(81)90599-5 [5] 张年梅,杨桂通.非线性弹性梁中的混沌带现象[J].应用数学和力学,2003,24(5):450—454. [6] 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].Kamihama:Mie University Press, 1997, 279—284. -
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