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

The Dynamics of the Slow Flow of a Singular Damped Nonlinear System and It Parametric Study

Journal of Applied Nonlinear Dynamics 3(1) (2014) 37--49 | DOI:10.5890/JAND.2014.03.004

J.O. Maaita$^{1}$; E. Meletlidou$^{1}$; A.F. Vakakis$^{2}$; V. Rothos$^{3}$

$^{1}$ Physics Department, Aristotle University of Thessaloniki, Greece

$^{2}$ Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, United States

$^{3}$ Department of Mathematics, Physics and Computational Sciences, Faculty of Technology, Aristotle University of Thessaloniki, Thessaloniki, Greece

Abstract

We study the dynamical behavior of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an essentially nonlinear attachment and compare the behavior of the initial system to the Slow Invariant Manifold (SIM). The dynamics of the slow flow can be simple, making regular oscillations in the region of the stable branches of the SIM, having relaxation oscillations or chaotic behavior.The initial system oscillates in the region of the SIM, verifying that the SIM plays an essential role for the dynamics of the initial system.

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