耦合非线性振子链的周期性驱动动力学研究（英文）

发布时间：2018-12-14 16:18

【摘要】：目的:考虑一个包含Duffing型非线性、粘性阻尼和运动谐波激励的一维耦合振子链,本文旨在推导描述振幅和相位的近似方程,得到并检验两类基本共振态(同振和反向共振)发生的条件,同时分析模型参数对同步率的影响。创新点:1.利用时间序列的互相关测量特定振子间的相互蝶,并通过一系列的数值实验来验证理论预测的结果;2.给出考虑干摩擦的系统共振的一些简要说明。方法:1.采用经典的平均值法进行理论分析;2.采用MEBDFV求解器计算多自由系统的数值解。结论:1.利用平均值法确定了两种共振现象:同相状态(低频激励)和反相状态(高频激励);2.关于同相共振的预测非常琐碎但对多自由度的振子链非常适用;3.对于反相共振的预测适用于短的振子链;4.可以通过改变系统的物理参数来提高同步率。
[Abstract]:Aim: to consider a one-dimensional coupled oscillator chain with Duffing type nonlinear, viscous damping and motion harmonic excitation. In this paper, an approximate equation describing amplitude and phase is derived. The conditions for the occurrence of two kinds of basic resonance states (common resonance and reverse resonance) are obtained and tested. The influence of model parameters on the synchronization rate is analyzed at the same time. Innovation: 1. The cross correlation of time series is used to measure the mutual butterflies between certain oscillators, and a series of numerical experiments are carried out to verify the predicted results. 2. Some brief explanations of system resonance considering dry friction are given. Methods: 1. The classical mean value method is used for theoretical analysis. 2. The MEBDFV solver is used to calculate the numerical solution of the multi-free system. Conclusion: 1. Two kinds of resonance phenomena are determined by the mean value method: the in-phase state (low-frequency excitation) and the inverse-phase state (high-frequency excitation); 2. The prediction of in-phase resonance is trivial but suitable for multi-degree-of-freedom oscillator chains. The prediction of inverse phase resonance is suitable for short oscillator chains. The synchronization rate can be improved by changing the physical parameters of the system.
【作者单位】： Institute
【基金】：supported by the Polish National Science Center under the Grant MAESTRO 2(No.2012/04/A/ST8/00738)for years 2012 2016
【分类号】：O313;O32

【相似文献】