耦合非线性振子链的周期性驱动动力学研究（英文）  

Dynamics of a periodically driven chain of coupled nonlinear oscillators

作　　者：Roman STAROSTA Jan AWREJCEWICZ Pawet FRITZKOWSKI Grazyna SYPNIEWSKA-KAMINSKA 

机构地区：[1]Institute of Applied Mechanics, Poznan University of Technology, Poznan 60-965, Poland [2]Department of Automatics and Biomechanics, Technical University of Ldd2, Ldd2 90-924, Poland

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2017年第7期497-510,共14页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：supported by the Polish National Science Center under the Grant MAESTRO 2(No.2012/04/A/ST8/00738)for years 2012–2016

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。A 1D chain of coupled oscillators is considered, including the Duffing-type nonlinearity, viscous damping, and kinematic harmonic excitation. The equations of motion are presented in a non-dimensional form. The approximate equations for the vibrational amplitudes and phases are derived by means of the classical averaging method. A simple analysis of the resulting equations allows one to determine the conditions for the two basic synchronous steady-states of the system： the in-phase and anti-phase motions. The relations between the required excitation frequency and the natural frequencies of the abbreviated （linear） system are discussed. The validity of these predictions is examined by a series of numerical experiments. The effect of the model parameters on the rate of synchronization is analyzed. For the purpose of systematic numerical studies, the cross-correlation of time-series is used as a measure of the phase adjustment between particular oscillators. Finally, some essential issues that arise in case of the mechanical system with dry friction axe indicated.

关 键 词：耦合非线性振子 同步运动 平均值法 

分 类 号：O313[理学—一般力学与力学基础] O32[理学—力学]