考虑耗散效应的金属杆受扰动后的非线性动力学现象分析

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．

Nonlinear Complex Dynamic Phenomena of the Perturbed Metallic Bar Considering Dissipating Effect

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.