Experimental study of impact oscillator with one-sided elastic constraint

James Ing, Ekaterina Pavlovskaia, Marian Wiercigroch, Soumitro Banerjee

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75 Citations (Scopus)

Abstract

In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

Original languageEnglish
Pages (from-to)679-705
Number of pages26
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume366
Issue number1866
Early online date18 Oct 2007
DOIs
Publication statusPublished - 13 Mar 2008

Keywords

  • impact oscillator
  • experimental chaos
  • grazing
  • stability of limit cycles
  • piecewise-linear-oscillator
  • grazing-incidence
  • border-collision
  • dynamics
  • bifurcations
  • systems
  • motions
  • chaos
  • verification
  • behavior

Cite this

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title = "Experimental study of impact oscillator with one-sided elastic constraint",
abstract = "In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.",
keywords = "impact oscillator, experimental chaos, grazing, stability of limit cycles, piecewise-linear-oscillator, grazing-incidence, border-collision, dynamics, bifurcations, systems, motions, chaos, verification, behavior",
author = "James Ing and Ekaterina Pavlovskaia and Marian Wiercigroch and Soumitro Banerjee",
year = "2008",
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language = "English",
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T1 - Experimental study of impact oscillator with one-sided elastic constraint

AU - Ing, James

AU - Pavlovskaia, Ekaterina

AU - Wiercigroch, Marian

AU - Banerjee, Soumitro

PY - 2008/3/13

Y1 - 2008/3/13

N2 - In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

AB - In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

KW - impact oscillator

KW - experimental chaos

KW - grazing

KW - stability of limit cycles

KW - piecewise-linear-oscillator

KW - grazing-incidence

KW - border-collision

KW - dynamics

KW - bifurcations

KW - systems

KW - motions

KW - chaos

KW - verification

KW - behavior

U2 - 10.1098/rsta.2007.2122

DO - 10.1098/rsta.2007.2122

M3 - Article

VL - 366

SP - 679

EP - 705

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

SN - 1364-503X

IS - 1866

ER -