Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing

James Ing; Ekaterina Evgenievna Pavlovskaia; Marian Wiercigroch; Soumitro Banerjee

doi:10.1016/j.physd.2009.11.009

Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing

James Ing, Ekaterina Evgenievna Pavlovskaia, Marian Wiercigroch, Soumitro Banerjee

Indian Inst Sci Educ & Res

Research output: Contribution to journal › Article › peer-review

108 Citations (Scopus)

Abstract

In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	312-321
Number of pages	10
Journal	Physica. D, Nonlinear Phenomena
Volume	239
Issue number	6
Early online date	26 Nov 2009
DOIs	https://doi.org/10.1016/j.physd.2009.11.009
Publication status	Published - 15 Mar 2010

Bibliographical note

A paid open access option is available for this journal.
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Voluntary deposit by author of authors post-print allowed on institutions open scholarly website including Institutional Repository
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Keywords

Piecewise linear oscillator
Grazing
Experimental study
Stability analysis
Border collision bifurcations
Piecewise-linear-oscillator
Sytems
Dynamics
Maps

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Cite this

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title = "Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing",

abstract = "In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.",

keywords = "Piecewise linear oscillator, Grazing, Experimental study, Stability analysis, Border collision bifurcations, Piecewise-linear-oscillator, Sytems, Dynamics, Maps",

author = "James Ing and Pavlovskaia, {Ekaterina Evgenievna} and Marian Wiercigroch and Soumitro Banerjee",

note = "A paid open access option is available for this journal. Voluntary deposit by author of pre-print allowed on Institutions open scholarly website and pre-print servers Voluntary deposit by author of authors post-print allowed on institutions open scholarly website including Institutional Repository Deposit due to Funding Body, Institutional and Governmental mandate only allowed where separate agreement between repository and publisher exists Set statement to accompany deposit Published source must be acknowledged Must link to journal home page or articles' DOI Publisher's version/PDF cannot be used Articles in some journals can be made Open Access on payment of additional charge NIH Authors articles will be submitted to PubMed Central after <num>12</num> <period units={"}month{"}>months</period> Authors who are required to deposit in subject-based repositories may also use Sponsorship Option ",

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AU - Banerjee, Soumitro

N1 - A paid open access option is available for this journal. Voluntary deposit by author of pre-print allowed on Institutions open scholarly website and pre-print servers Voluntary deposit by author of authors post-print allowed on institutions open scholarly website including Institutional Repository Deposit due to Funding Body, Institutional and Governmental mandate only allowed where separate agreement between repository and publisher exists Set statement to accompany deposit Published source must be acknowledged Must link to journal home page or articles' DOI Publisher's version/PDF cannot be used Articles in some journals can be made Open Access on payment of additional charge NIH Authors articles will be submitted to PubMed Central after <num>12</num> <period units="month">months</period> Authors who are required to deposit in subject-based repositories may also use Sponsorship Option

PY - 2010/3/15

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N2 - In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.

AB - In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.

KW - Piecewise linear oscillator

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KW - Experimental study

KW - Stability analysis

KW - Border collision bifurcations

KW - Piecewise-linear-oscillator

KW - Sytems

KW - Dynamics

KW - Maps

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JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

IS - 6

ER -

Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing

Abstract

Bibliographical note

Keywords

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