Journal ArticleDOI
Evidences of global bifurcations of an imperfect circular plate
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TLDR
In this article, the global bifurcations in modal interactions of an imperfect circular plate with one-to-one internal resonance were investigated, and the equations governing nonlinear oscillations of the plate were reduced to a system of non-autonomous ordinary differential equations via Galerkin's procedure.About:
This article is published in Journal of Sound and Vibration.The article was published on 2006-05-30. It has received 21 citations till now. The article focuses on the topics: Nonlinear Oscillations & Ordinary differential equation.read more
Citations
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Journal ArticleDOI
Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt
M. H. Yao,Wei Zhang,Jean W. Zu +2 more
TL;DR: In this article, the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear, nonplanar oscillations of the parametrically excited viscoelastic moving belt using an extended Melnikov method in the resonant case were investigated.
Journal ArticleDOI
Detecting multi-pulse chaotic dynamics of high-dimensional non-autonomous nonlinear system for circular mesh antenna
TL;DR: In this article, the authors investigated the global bifurcations and multi-pulse jumping chaotic dynamics of circular mesh antenna and employed an equivalent continuum circular cylindrical shell to represent the antenna.
Journal ArticleDOI
Multi-Pulse Shilnikov Chaotic Dynamics for a Non-Autonomous Buckled Thin Plate under Parametric Excitation
Journal ArticleDOI
Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation
Weiqin Yu,Fangqi Chen +1 more
TL;DR: In this paper, the global bifurcations in mode interaction of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation are investigated with the case of the 1:1 internal resonance, the average equations representing the evolution of the amplitudes and phases of the interacting normal modes exhibiting complex dynamics.
Journal ArticleDOI
Global bifurcations and chaos in a harmonically excited and undamped circular plate
Sergey B. Samoylenko,W.K. Lee +1 more
TL;DR: In this paper, the authors investigated global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance, in which an excitation frequency is near natural frequencies, and the damping force is not included in the analysis.
References
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Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
Book
Global Bifurcations and Chaos: Analytical Methods
TL;DR: Global Bifurcations and Chaos: Analytical Methods as discussed by the authors describes the mechanisms which give rise to chaos and derives explicit techniques whereby these mechanisms can be detected in specific systems.
Journal ArticleDOI
Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
Gregor Kovačič,Stephan Wiggins +1 more
TL;DR: In this article, the authors developed new global perturbation techniques for detecting homoclinic trajectories in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two-degree-of-freedom Hamiltonian systems.
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Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
Gregor Kovačič,Stephan Wiggins +1 more