Dynamics of a cubic nonlinear vibration absorber
type: Item
instance of: scholarly article
title: Dynamics of a cubic nonlinear vibration absorber
zbMATH Open document ID: 0966.70014
DOI: 10.1023/A:1008358825502
author: Shafic S. Oueini
author: Char-Ming Chin
author: A. H. Nayfeh
published in: Nonlinear Dynamics
publication date: 2001-05-31T00:00:00Z
review text: This paper deals with the practically important phenomenon of vibration absorption, i.e. the dissipation-free suppression of a forced vibration. This effect is usually achieved making use of the fact that oscillatory systems coupled with quadratic nonlinearities possess a 2:1 internal resonance for which a saturation phenomenon exists. The authors of this interesting and very well written paper study the saturation phenomenon in systems where the coupling is done with cubic terms instead of quadratic ones. Using the method of multiple scales, the authors construct approximate solutions to nonlinear equations of motion. A bifurcation analysis of solutions is performed, and a small domain of existence of saturation phenomenon is calculated. Additionally, the authors prove the existence of more complicated dynamic behavior.
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 1439509
zbMATH Keywords: vibration absorption
zbMATH Keywords: 2:1 internal resonance
zbMATH Keywords: saturation phenomenon
zbMATH Keywords: cubic terms
zbMATH Keywords: method of multiple scales
zbMATH Keywords: approximate solutions
zbMATH Keywords: bifurcation analysis
reviewed by: Hans Troger
MaRDI profile type: Publication
full work available at URL: a:1008358825502
OpenAlex ID: W111342554
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description: scientific article; zbMATH DE number 1439509