Perturbation-iterative method for determining limit cycles of strongly non-linear oscillators

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)707-717
Journal / PublicationJournal of Sound and Vibration
Volume183
Issue number4
Publication statusPublished - 1 Jan 1995

Abstract

A perturbation-iterative method is presented for determining limit cycles of strongly non-linear oscillators of the form x.. + g(x) =Q μf(x,x.), where g(x) is an arbitrary non-linear function of the displacement x, and μ has a small to moderate value. By assuming that x = a cos φ + b and dφ /dt = Φ (φ), where Φ (φ) is 2π-periodic in φ, the method allows a, b and Φ (φ) to be calculated to any desired degree of accuracy by the iterative method, and the limit cycle phase portraits are in very good agreement with the corresponding numerical solutions of the differential equations.