Amplitude modulated chaos in two-degree-of-freedom systems with quadratic nonlinearities
type: Item
instance of: scholarly article
title: Amplitude modulated chaos in two-degree-of-freedom systems with quadratic nonlinearities
zbMATH Open document ID: 0908.70022
DOI: 10.1007/BF01213022
author: D. Massart
published in: Acta Mechanica
publication date: 1999-03-10T00:00:00Z
review text: The authors investigate two-degree-of-freedom systems with weak quadratic nonlinearities in the presence of 1:2 internal resonance. All six possible cases of external or parametric/combination resonance are considered. A set of four first-order equations is obtained by the method of averaging. For the averaged system without damping, using Melnikov's method, the authors present the parameter range which chaotic dynamics exists. In the presence of damping this analytical approach does not work, but numerical studies show the persistence of chaotic responses.
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70K28
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1143324
zbMATH Keywords: 1:2 internal resonance
zbMATH Keywords: four first-order equations
zbMATH Keywords: method of averaging
zbMATH Keywords: Melnikov's method
reviewed by: S. Yanchuk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1143324