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A Method for Obtaining Approximate Analytic Periods for a Class of Nonlinear Oscillators

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Abstract

This paper deals with nonlinear oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we establish two approximate analytic formulas for the period. These two formulas are valid for small as well as large amplitudes of oscillation. Three examples are used to illustrate that the proposed formulas can give very satisfactory approximate results.

Sommario. Questo lavoro tratta il problema delle oscillazioni nonlineari di sistemi conservativi ad un grado di libertà con nonlinearità simmetriche. Combinando opportunamente la tecnica di linearizzazione dell'equazione del moto con il metodo del bilancio armonico si perviene a due formule analitiche approssimate per il periodo. Le formule ottenute sono valide sia per piccole che per grandi ampiezze di oscillazione. Si utilizzano tre esempi classici di oscillatori nonlineari per illustrate l'efficacia del metodo nel produrre risultati approssimati soddisfacenti.

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Authors and Affiliations

  1. Department of Mathematics, Mechanics Section, Jilin University, Changchun, 130012, P. R. China

    Baisheng Wu & Pengsong Li

Authors
  1. Baisheng Wu
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  2. Pengsong Li
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Wu, B., Li, P. A Method for Obtaining Approximate Analytic Periods for a Class of Nonlinear Oscillators. Meccanica 36, 167–176 (2001). https://doi.org/10.1023/A:1013067311749

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  • DOI: https://doi.org/10.1023/A:1013067311749

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