On various representations of higher order approximations of the free oscillatory response of nonlinear dynamical systems

Harry Dankowicz, Walter Lacarbonara

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates the flexibility afforded by the application of regular perturbation methods (in particular, the method of multiple scales) for the purpose of obtaining higher order approximations of the oscillatory response of a nonlinear dynamical system. It is shown that the non-uniqueness of these higher order approximations can be removed by enforcing additional conditions while the relationship between the frequency of oscillation and measurable quantities (the Hamiltonian, the time-averaged kinetic or stored energy) is unique and is thus not affected by these additional conditions.

Original languageEnglish (US)
Pages (from-to)3410-3423
Number of pages14
JournalJournal of Sound and Vibration
Volume330
Issue number14
DOIs
StatePublished - Jul 4 2011

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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