Free vibration analysis of a structural system with a pair of irrational nonlinearities

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)997-1007
Journal / PublicationApplied Mathematical Modelling
Publication statusPublished - 1 May 2017


An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.

Research Area(s)

  • Analytical approximate solutions, Harmonic balance method, Irrational nonlinearities, Newton's method, Rational approximation