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Author:

Yao, M. H. (Yao, M. H..) | Zhang, W. (Zhang, W..)

Indexed by:

EI Scopus SCIE

Abstract:

The Shilnikov-type multipulse orbits and chaotic dynamics for a simply supported rectangular thin plate under combined parametric and external excitations are studied in this paper for the first time. The rectangular thin plate is subjected to spatially and temporally varying transversal and in-plane excitations, simultaneously. The formulas of the rectangular thin plate are derived from the von Karman equation and Galerkin's method. The method of multiple scales is used to find the averaged equation in the case of 1: 2 internal resonance. Based on the averaged equation, the theory of normal form is used to obtain the explicit expressions of normal form associated with a double zero and a pair of purely imaginary eigenvalues using the Maple program. The dissipative version of the energy-phase method is utilized to analyze the multipulse global bifurcations and chaotic dynamics of a parametrically and externally excited rectangular thin plate. The global dynamical analysis indicates that there exist the multipulse jumping orbits in the perturbed phase space of the averaged equation for a parametrically and externally excited rectangular thin plate. These results show that the chaotic motions of the multipulse Shilnikov-type can occur for a parametrically and externally excited rectangular thin plate. Numerical simulation results are presented to verify the analytical predictions. It is also found from the results of numerical simulation that the Shilnikov-type multipulse orbits exist for a parametrically and externally excited thin plate.

Keyword:

normal form Shilnikov-type multipulse orbits parametric and external excitations rectangular thin plate chaotic dynamics

Author Community:

  • [ 1 ] Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China

Reprint Author's Address:

  • 张伟

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

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Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2007

Issue: 3

Volume: 17

Page: 851-875

2 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

JCR Journal Grade:2

Cited Count:

WoS CC Cited Count: 24

SCOPUS Cited Count: 26

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 5

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