In the present study, a modified model is introduced to estimate the structural oscillation ampli- tude of a circular cylinder during lock-in in the vortex-induced vibration phenomenon. The modified model includes the same van der Pol term as in the classic model, while its coefficients are assumed to be variable. This modified model is utilized to bring about compliance between theoretical solution and experimental results. Then, a fifth-order aerodynamic term is added, and the coefficients are modified and optimized using a new straightforward solution method. Here, the displacement, velocity and acceleration coupling terms are used to solve the system of equations. The response of the coupled equations is assumed to be harmonic. A linear approach is adopted to simplify and derive the solutions algebraically. The results are plotted during lock-in for amplitude as a function of reduced velocity and for maximum structural oscillation amplitude versus Skop–Griffin parameter. Finally, these results are compared with those of the classic wake oscillator model. The present modified model evinces an exact compliance with experimental measurements regarding structural oscillation amplitude, lock-in range, some hysteresis and mass damping ratio attributes, and reduces sensitivity to the type of coupling term through adding the fifth-order damping term.

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