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Author:

Zhang, W (Zhang, W.) | Wang, FX (Wang, FX.) | Yao, MH (Yao, MH.)

Indexed by:

EI Scopus SCIE

Abstract:

This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.

Keyword:

normal form parametric and external excitations global bifurcations cantilever beam chaotic dynamics nonlinear nonplanar oscillations

Author Community:

  • [ 1 ] Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China
  • [ 2 ] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

Reprint Author's Address:

  • 张伟

    [Zhang, W]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China

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Source :

NONLINEAR DYNAMICS

ISSN: 0924-090X

Year: 2005

Issue: 3

Volume: 40

Page: 251-279

5 . 6 0 0

JCR@2022

ESI Discipline: ENGINEERING;

JCR Journal Grade:2

Cited Count:

WoS CC Cited Count: 94

SCOPUS Cited Count: 103

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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