Global bifurcations of symmetric cross‐ply composite laminated plates with 1:2 internal resonance

Global bifurcations of symmetric cross‐ply composite laminated plates with 1:2 internal resonance This paper investigates the global bifurcations and chaotic dynamics for nonlinear oscillations of symmetric cross‐ply composite laminated plates in case of 1:2 internal resonance. The higher‐dimensional Melnikov method and its extensions developed by Kovac˘ic˘ and Wiggins is employed to analyze the global bifurcations for composite laminated plates. The explicitly sufficient conditions of the existence of Silnikov‐type homoclinic orbits in perturbed phase space are gained, which may lead to chaotic motions for composite laminated plates. Finally, numerical results obtained by fourth‐order Runge‐Kutta method also indicate that there exist the jumping phenomena and chaotic responses for the nonlinear composite laminated plates, which agree with theoretic predictions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zamm-Zeitschrift Fuer Angewandte Mathematik Und Mechanik Wiley

Global bifurcations of symmetric cross‐ply composite laminated plates with 1:2 internal resonance

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
ISSN
0044-2267
eISSN
1521-4001
D.O.I.
10.1002/zamm.201600049
Publisher site
See Article on Publisher Site

Abstract

This paper investigates the global bifurcations and chaotic dynamics for nonlinear oscillations of symmetric cross‐ply composite laminated plates in case of 1:2 internal resonance. The higher‐dimensional Melnikov method and its extensions developed by Kovac˘ic˘ and Wiggins is employed to analyze the global bifurcations for composite laminated plates. The explicitly sufficient conditions of the existence of Silnikov‐type homoclinic orbits in perturbed phase space are gained, which may lead to chaotic motions for composite laminated plates. Finally, numerical results obtained by fourth‐order Runge‐Kutta method also indicate that there exist the jumping phenomena and chaotic responses for the nonlinear composite laminated plates, which agree with theoretic predictions.

Journal

Zamm-Zeitschrift Fuer Angewandte Mathematik Und MechanikWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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