Asymptotic analysis and accurate approximate solutions for strongly nonlinear conservative symmetric 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)243-254
Journal / PublicationApplied Mathematical Modelling
Online published9 May 2017
Publication statusPublished - Sep 2017


A new accurate iterative and asymptotic method is introduced to construct analytical approximate solutions to strongly nonlinear conservative symmetric oscillators. The method is based on applying a second-order expansion with the harmonic balance method and it excludes the requirement of solving a set of coupled nonlinear algebraic equations. Newton's iteration or the linearized model may be readily deduced by considering only the first-order terms in the model. According to this iterative approach, only Fourier series expansions of restoring force function, its first- and second-order derivatives for each iteration are required. It is concluded here that by only one single iteration, very brief and yet accurate analytical approximate solutions can be attained. Three physical examples are solved and accurate solutions are presented to illustrate the physics of the system and the effectiveness of the proposed asymptotic method.

Research Area(s)

  • Analytical approximation, Conservative symmetric oscillator, Harmonic balance, Nonlinear dynamic system, Second-order Newton iteration