Vibrations of an elastically mounted rigid cylinder excited by steady fluid flow are studied. Because of nonlinearity of real structures, in the present study, dynamic behaviour of the cylinder is described by double Duffing equations and using the quadratic terms, the wake oscillator equations are coupled. Regarding to this approach, the combined cross-flow and in-line Vortex Induced Vibrations (VIV) of the cylinder is modelled in a more accurate manner. Empirical coefficients are adjusted through comparison with previous credible experimental studies. Finally, effects of changing coefficients of the quadratic terms on major VIV parameters are investigated.

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