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Author:

Li, S. B. (Li, S. B..) | Zhang, W. (Zhang, W..) | Yao, M. H. (Yao, M. H..)

Indexed by:

EI Scopus SCIE

Abstract:

Global bifurcations and Shilnikov type multipulse chaotic dynamics for a nonlinear vibration absorber are investigated by using the energy-phase method for the first time. A two-degree-of-freedom model of a nonlinear vibration absorber is considered. After the nonlinear nonautonomous equations of this model are given, the method of multiple scales is used to derive four first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases of the two interacting modes in the presence of 1:1 internal resonance and primary resonance. Using several coordinate transformations to transform the modulation equation into a standard form, we can apply the energy-phase method to show the existence of the multipulse chaotic dynamics by identifying Shilnikov-type multipulse orbits in the perturbed phase space. We are able to obtain the explicit restriction on the damping, forcing excitation and the detuning parameters, under which the multipulse chaotic dynamics is expected. These multipulse orbits represent the repeated departure from purely vertical oscillations for the nonlinear vibration absorber. Numerical simulations also indicate that there exist different forms of the multipulse chaotic responses and jumping phenomena for the nonlinear vibration absorber.

Keyword:

chaotic dynamics Shilnikov type multipulse orbits Nonlinear vibration absorber energy-phase method

Author Community:

  • [ 1 ] [Li, S. B.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 2 ] [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 3 ] [Yao, M. H.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

Reprint Author's Address:

  • 张伟

    [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

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Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2012

Issue: 1

Volume: 22

2 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 8

SCOPUS Cited Count: 8

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 7

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