Rotational galloping of two coupled oscillators
type: Item
instance of: scholarly article
title: Rotational galloping of two coupled oscillators
zbMATH Open document ID: 0923.70018
DOI: 10.1023/A:1004382612765
author: T. I. Haaker
author: A. H. P. Van Der Burgh
published in: Meccanica
publication date: 1999-11-01T00:00:00Z
review text: The authors consider nonlinear rotational galloping for two mechanically coupled see-saw oscillators in steady cross-flow, and they obtain two nonlinearly coupled harmonic oscillators using a quasi-steady modelling approach. The authors find either a non-resonant (for strong coupling) or 1:1 internal resonant system (for weak coupling) depending on \(K\), the order of the mechanical coupling, and on the difference \(\delta\) between the natural frequencies of the uncoupled oscillators. The averaged equations in the case of weak coupling allow stable limit cycles which arise in symmetrical pairs and are born by Hopf bifurcations. In addition, numerical calculations suggest that for certain parameter values these cycles may merge into large symmetrical limit cycles, and that all the limit cycles found for the averaged equations correspond to solutions with periodically modulated amplitudes and phases for the original system.
Mathematics Subject Classification ID: 70K99
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 74F10
zbMATH DE Number: 1240529
zbMATH Keywords: non-resonant system
zbMATH Keywords: steady cross-flow
zbMATH Keywords: quasi-steady modelling approach
zbMATH Keywords: 1:1 internal resonant system
zbMATH Keywords: averaged equations
zbMATH Keywords: weak coupling
zbMATH Keywords: stable limit cycles
zbMATH Keywords: Hopf bifurcations
MaRDI profile type: Publication
full work available at URL: a:1004382612765
OpenAlex ID: W126737711
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description: scientific article; zbMATH DE number 1240529