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CLC number: O313; O32

On-line Access: 2017-07-04

Received: 2016-09-15

Revision Accepted: 2017-02-16

Crosschecked: 2017-06-12

Cited: 0

Clicked: 1026

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Paweł Fritzkowski

http://orcid.org/0000-0003-1374-2364

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Journal of Zhejiang University SCIENCE A 2017 Vol.18 No.7 P.497-510

10.1631/jzus.A1600628


Dynamics of a periodically driven chain of coupled nonlinear oscillators


Author(s):  Paweł Fritzkowski, Roman Starosta, Grażyna Sypniewska-Kamińska, Jan Awrejcewicz

Affiliation(s):  Institute of Applied Mechanics, Poznań University of Technology, Poznań 60-965, Poland; more

Corresponding email(s):   pawel.fritzkowski@put.poznan.pl

Key Words:  Nonlinear coupled oscillators, Synchronous motion, Averaging method


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Paweł Fritzkowski, Roman Starosta, Grażyna Sypniewska-Kamińska, Jan Awrejcewicz. Dynamics of a periodically driven chain of coupled nonlinear oscillators[J]. Journal of Zhejiang University Science A, 2017, 18(1): 497-510.

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Abstract: 
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.

耦合非线性振子链的周期性驱动动力学研究

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求解器计算多自由度系统的数值解。
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。

关键词:耦合非线性振子;同步运动;平均值法

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