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

http://doi.org/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):  1. 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(7): 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.

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Full Text:   <4463>

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CLC number: O313; O32

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2017-06-12

Cited: 0

Clicked: 7211

Citations:  Bibtex RefMan EndNote GB/T7714

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