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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Global Dynamics Analysis of a Continuum Rotor through G-Function and L-Function Method

Journal of Applied Nonlinear Dynamics 5(2) (2016) 127--146 | DOI:10.5890/JAND.2016.06.001

Haiyang Luo$^{1}$,$^{2}$; Yuefang Wang$^{1}$,$^{2}$

$^{1}$ Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

$^{2}$ State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian 116024, China

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Abstract

The global dynamics of a continuum rotor excited by nonlinear oilfilm force and electromagnetic force is investigated. The governing equation of the system is obtained using the Galerkin’s method. The dynamical systems are reduced into two 2-dimensional systems in Yand Z-directions. The analytical conditions for global transversality and tangency to the separatrix are presented. The global and local dynamics of the system is determined through the G-function and G(1)-function and is compared to numerical solution. The periodicity of periodic flow of the rotor is determined by the L-function. The complexity of the nonlinear continuum rotor system is demonstrated through global transversality and tangency of the periodic motions to separatrix.

Acknowledgments

The supports from Free Exploration Project of State Key Laboratory of Structural Analysis for Industrial Equipment (Grant S14204), Liaoning Provincial Program for Science and Technology (Grants 201303002, 2014028004), and the State Key Development Program for Basic Research of China (Grant 2015CB057300) are gratefully acknowledged.

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