Subharmonic orbits of a strongly nonlinear oscillator forced by closely spaced harmonics

Themistoklis P. Sapsis, Alexander F. Vakakis

Research output: Contribution to journalArticle

Abstract

We study asymptotically the family of subharmonic responses of an essentially nonlinear oscillator forced by two closely spaced harmonics. By expressing the original oscillator in action-angle form, we reduce it to a dynamical system with three frequencies (two fast and one slow), which is amenable to a singular perturbation analysis. We then restrict the dynamics in neighborhoods of resonance manifolds and perform local bifurcation analysis of the forced subharmonic orbits. We find increased complexity in the dynamics as the frequency detuning between the forcing harmonics decreases or as the order of a secondary resonance condition increases. Moreover, we validate our asymptotic results by comparing them to direct numerical simulations of the original dynamical system. The method developed in this work can be applied to study the dynamics of strongly nonlinear (nonlinearizable) oscillators forced by multiple closely spaced harmonics; in addition, the formulation can be extended to the case of transient excitations.

Original languageEnglish (US)
Article number011014
JournalJournal of Computational and Nonlinear Dynamics
Volume6
Issue number1
DOIs
StatePublished - Jan 1 2011

Fingerprint

Subharmonics
Nonlinear Oscillator
Orbits
Harmonic
Orbit
Dynamical systems
Dynamical system
Local Bifurcations
Perturbation Analysis
Direct numerical simulation
Bifurcation Analysis
Singular Perturbation
Forcing
Excitation
Angle
Decrease
Formulation

Keywords

  • Asymptotic analysis
  • Forced strongly nonlinear oscillator

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Subharmonic orbits of a strongly nonlinear oscillator forced by closely spaced harmonics. / Sapsis, Themistoklis P.; Vakakis, Alexander F.

In: Journal of Computational and Nonlinear Dynamics, Vol. 6, No. 1, 011014, 01.01.2011.

Research output: Contribution to journalArticle

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