Table of Contents
Journal of Nonlinear Dynamics
Volume 2014, Article ID 208171, 10 pages
http://dx.doi.org/10.1155/2014/208171
Research Article

The Effect of Slow Invariant Manifold and Slow Flow Dynamics on the Energy Transfer and Dissipation of a Singular Damped System with an Essential Nonlinear Attachment

Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Received 30 May 2014; Revised 23 July 2014; Accepted 26 July 2014; Published 1 September 2014

Academic Editor: Mitsuhiro Ohta

Copyright © 2014 Jamal-Odysseas Maaita and Efthymia Meletlidou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the effect of slow flow dynamics and slow invariant manifolds on the energy transfer and dissipation of a dissipative system of two linear oscillators coupled with an essential nonlinear oscillator with a mass much smaller than the masses of the linear oscillators. We calculate the slow flow of the system, the slow invariant manifold, the total energy of the system, and the energy that is stored in the nonlinear oscillator for different sets of the parameters and show that the bifurcations of the SIM and the dynamics of the slow flow play an important role in the energy transfer from the linear to the nonlinear oscillator and the rate of dissipation of the total energy of the initial system.