Impulsive periodic and quasi-periodic orbits of coupled oscillators with essential stiffness nonlinearity

Gaetan Kerschen, Oleg Gendelman, Alexander F. Vakakis, Lawrence Bergman, D. Michael McFarland

Research output: Contribution to journalArticlepeer-review

Abstract

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi-periodic dynamics of the undamped system forced by a single impulse on the linear oscillator and being initially at rest, by considering separately low-, moderate- and high-energy impulsive motions. The motivation for studying the impulsive dynamics of this system centers on passive targeted energy transfer properties of the corresponding weakly damped one, that is, of the possibility of one-way, irreversible transfer of energy from the linear oscillator to the nonlinear attachment. A rather surprising aspect of this work is the complexity of the analysis required to study the impulsive dynamics of this system, due to its high degeneracy, as it undergoes a co-dimension three bifurcation.

Original languageEnglish (US)
Pages (from-to)959-978
Number of pages20
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume13
Issue number5
DOIs
StatePublished - Jul 1 2008
Externally publishedYes

Keywords

  • Coupled oscillators
  • Impulsive responses
  • Targeted energy transfer

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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