Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations
type: Item
instance of: scholarly article
title: Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations
zbMATH Open document ID: 0969.70017
DOI: 10.1023/A:1008315706651
published in: Nonlinear Dynamics
publication date: 2001-10-01T00:00:00Z
review text: This paper studies dynamic response of a one-degree-of-freedom system with both quadratic and cubic nonlinearities, subjected to combined parametric and external excitations with incommensurate frequencies. Such model can describe one-mode vibrations of a heavy elastic structure suspended between two fixed supports at the same level and excited by a longitudinal and transversal periodic forces. From physical point of view, the quadratic term is present due to the curvature of the structure, whereas the cubic term is due to the symmetric nonlinearity of the material. By using the Bogolyubov-Mitropolskij method, the authors transform the original quasi-periodic system to a reduced system. The solution of the reduced system is then obtained by small parameter method which provides nonlinear approximations to the periodic solution. Finally, the authors construct a control of chaos by introducing a harmonic parametric component into the cubic term.
reviewed by: Yuri N. Sankin
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 70K43
zbMATH DE Number: 1342558
zbMATH Keywords: parametric excitation
zbMATH Keywords: external excitation
zbMATH Keywords: one-mode vibrations of elastic structure
zbMATH Keywords: one-degree-of-freedom system
zbMATH Keywords: quadratic term
zbMATH Keywords: cubic term
zbMATH Keywords: Bogolyubov-Mitropolskij method
zbMATH Keywords: reduced system
zbMATH Keywords: small parameter method
zbMATH Keywords: nonlinear approximations
zbMATH Keywords: control of chaos
author: Mohamed Belhaq
author: Mohamed Houssni
MaRDI profile type: Publication
full work available at URL: a:1008315706651
OpenAlex ID: W271319212
Recommended article: Suppression of chaos in a nonlinear oscillator with parametric and external excitation
Recommended article: Suppression of chaos in averaged oscillator driven by external and parametric excitations
Recommended article: Chaos in a Weakly Nonlinear Oscillator With Parametric and External Resonances
Recommended article: A quasi-periodic route to chaos in a parametrically driven nonlinear medium
Recommended article: Chaotic Motions of a Duffing Oscillator Subjected to Combined Parametric and Quasiperiodic Excitation
Recommended article: THE LOSS OF CHAOS IN A QUASIPERIODICALLY-FORCED NONLINEAR OSCILLATOR
Recommended article: Q4730508
Recommended article: Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator
Recommended article: A Unified Approach to Chaos Suppressing and Inducing in a Periodically Forced Family of Nonlinear Oscillators
description: scientific article; zbMATH DE number 1342558