Accurate higher-order analytical approximate solutions to large-amplitude oscillating systems with a general non-rational restoring force

C. W. Lim, Siu Kai Lai, B. S. Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


A new approximate analytical approach for accurate higher-order nonlinear solutions of oscillations with large amplitude is presented in this paper. The oscillatory system is subjected to a non-rational restoring force. This approach is built upon linearization of the governing dynamic equation associated with the method of harmonic balance. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. This approach also explores large parameter regions beyond the classical perturbation methods which in principle are confined to problems with small parameters. It has significant contribution as there exist many nonlinear problems without small parameters. Through some examples in this paper, we establish the general approximate analytical formulas for the exact period and periodic solution which are valid for small as well as large amplitudes of oscillation.
Original languageEnglish
Pages (from-to)267-281
Number of pages15
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - 1 Nov 2005
Externally publishedYes


  • Harmonic balance method
  • Large amplitude
  • Linearization
  • Nonlinear oscillation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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