The University of Southampton
University of Southampton Institutional Repository

Resonances of the SD oscillator due to the discontinuous phase

Resonances of the SD oscillator due to the discontinuous phase
Resonances of the SD oscillator due to the discontinuous phase
Resonance phenomena of a harmonically excited system with mul-tiple potential well play an important role in nonlinear dynamics research.
In this paper, we investigate the resonant behaviours of a discontinuous dynamical system with double well potential derived from the SD oscillator to gain better understanding of the transition of resonance mechanism. Firstly,
the time dependent Hamiltonian is obtained for a Duffing type discontinuous system modelling snap-through buckling. This system comprises two subsystems connected at x = 0, for which the system is discontinuous. We construct
a series of generating functions and canonical transformations to obtain the canonical form of the system to investigate the complex resonant behaviours
of the system. Furthermore, we introduce a composed winding number to explore complex resonant phenomena. The formulation for resonant phenomena given in this paper generalizes the formulation of n Omega0 = m Omega used in the regular perturbation theory, where n and m are relative prime integers, Omega 0 and Omega are the natural frequency and external frequencies respectively. Understanding the resonant behaviour of the SD oscillator at the discontinuous
phase enables us to further reveal the vibrational energy transfer mechanism between smooth and discontinuous nonlinear dynamical systems
2156-907X
183-191
Cao, Qingjie
cd1f5d42-d297-42ff-a845-d02ee4066090
Xiong, Yeping
51be8714-186e-4d2f-8e03-f44c428a4a49
Wiercigroch, Marian
30f9b83b-4eb8-4ff0-a7e6-9cd22d34eca8
Cao, Qingjie
cd1f5d42-d297-42ff-a845-d02ee4066090
Xiong, Yeping
51be8714-186e-4d2f-8e03-f44c428a4a49
Wiercigroch, Marian
30f9b83b-4eb8-4ff0-a7e6-9cd22d34eca8

Cao, Qingjie, Xiong, Yeping and Wiercigroch, Marian (2011) Resonances of the SD oscillator due to the discontinuous phase. Journal of Applied Analysis and Computation, 1 (2), 183-191.

Record type: Article

Abstract

Resonance phenomena of a harmonically excited system with mul-tiple potential well play an important role in nonlinear dynamics research.
In this paper, we investigate the resonant behaviours of a discontinuous dynamical system with double well potential derived from the SD oscillator to gain better understanding of the transition of resonance mechanism. Firstly,
the time dependent Hamiltonian is obtained for a Duffing type discontinuous system modelling snap-through buckling. This system comprises two subsystems connected at x = 0, for which the system is discontinuous. We construct
a series of generating functions and canonical transformations to obtain the canonical form of the system to investigate the complex resonant behaviours
of the system. Furthermore, we introduce a composed winding number to explore complex resonant phenomena. The formulation for resonant phenomena given in this paper generalizes the formulation of n Omega0 = m Omega used in the regular perturbation theory, where n and m are relative prime integers, Omega 0 and Omega are the natural frequency and external frequencies respectively. Understanding the resonant behaviour of the SD oscillator at the discontinuous
phase enables us to further reveal the vibrational energy transfer mechanism between smooth and discontinuous nonlinear dynamical systems

PDF
JAAC_2011_QJYPMW_final.pdf - Version of Record
Download (3MB)

More information

Published date: May 2011

Identifiers

Local EPrints ID: 193115
URI: https://eprints.soton.ac.uk/id/eprint/193115
ISSN: 2156-907X
PURE UUID: e0e04936-2a8d-4c27-a434-c2d6a73902a4
ORCID for Yeping Xiong: ORCID iD orcid.org/0000-0002-0135-8464

Catalogue record

Date deposited: 12 Jul 2011 09:03
Last modified: 06 Jun 2018 12:51

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×