Dynamics of a periodically driven chain of coupled nonlinear oscillators
[ 1 ] Instytut Mechaniki Stosowanej, Wydział Budowy Maszyn i Zarządzania, Politechnika Poznańska | [ P ] pracownik
ZH 耦合非线性振子链的周期性驱动动力学研究
2017
artykuł naukowy
angielski
- nonlinear coupled oscillators
- synchronous motion
- averaging method
- 耦合非线性振子
- 同步运动
- 平均値法
EN 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 are indicated.
ZH
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,本文旨在推异描述振幅和相位的近似方程,得到并检验两类基木共振态(同相共振和反相共振)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位蝶,并通过一系列的数値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. 采用经典的平均値法进行理论分析; 2. 采用MEBDFV求解器计箅多自由度系统的数值解。
结论
1. 利用平均値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。
07.07.2017
497 - 510
20
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1,215