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

Siu Kai Lai, B. S. Wu, Y. Y. Lee

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)997-1007
Number of pages11
JournalApplied Mathematical Modelling
Publication statusPublished - 1 May 2017


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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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