Nonlinear Dynamics

, Volume 32, Issue 1, pp 1–13 | Cite as

A New Method for Approximate Analytical Solutions to Nonlinear Oscillations of Nonnatural Systems

  • B. S. Wu
  • C. W. Lim
  • L. H. He


This paper deals with nonlinear oscillations of a conservative,nonnatural, single-degree-of-freedom system with odd nonlinearity. Bycombining the linearization of the governing equation with the method ofharmonic balance, we establish approximate analytical solutions for thenonlinear oscillations of the system. Unlike the classical harmonicbalance method, the linearization is performed prior to proceeding withharmonic balancing thus resulting in linear algebraic equations insteadof nonlinear algebraic equations. Hence, we are able to establish theapproximate analytical formulas for the exact period and periodicsolution. These approximate solutions are valid for small as well aslarge amplitudes of oscillation. Two examples are presented toillustrate that the proposed formulas can give excellent approximateresults.

nonnatural system nonlinear oscillation odd nonlinearity linearization harmonic balance method 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • B. S. Wu
    • 1
  • C. W. Lim
    • 2
  • L. H. He
    • 3
  1. 1.Department of MathematicsJilin UniversityChangchunP.R. China
  2. 2.Department of Building and ConstructionCity University of Hong KongKowloonHong Kong, P.R. China
  3. 3.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiP.R. China

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