Energy transfers in a system of two coupled oscillators with essential nonlinearity: 1:1 Resonance manifold and transient bridging orbits

Gaetan Kerschen, Alexander F. Vakakis, Young S. Lee, D. Michael McFarland, Jeffrey J. Kowtko, Lawrence A. Bergman

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed.

Original languageEnglish (US)
Pages (from-to)283-303
Number of pages21
JournalNonlinear Dynamics
Volume42
Issue number3
DOIs
StatePublished - Nov 2005

Keywords

  • Energy transfer
  • Essential nonlinearity
  • Nonlinear beat phenomenon
  • Nonlinear energy pumping
  • Resonance capture

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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