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ObjectiveIn order to achieve the accurate prediction of the amplitude response of a vortex-induced vibrating cylinder under the sub-critical Reynolds number, a method for establishing a Cl-A/D (lift coefficient-amplitude ratio)model of the forced vibration of the cylinder by numerical simulation is proposed.MethodsBased on the Realizable k-ε model, a two-dimensional numerical simulation of the forced vibration of a cylinder is carried out using the finite volume method. The calculated lift coefficient curves under different amplitude ratios A/D in the range of excitation frequency ratio fe/fn=1 are obtained. The lift coefficient corresponding to the maximum vibration velocity of the cylinder is then selected to establish the Cl-A/D model. ResultsThe results show that the overall trend of the Cl-A/D fitting curve is in good agreement with the predicted results of SHEAR7. At the same time, it is found that the "zero lift coefficient" points under each excitation frequency ratio fe/fn are all located near the amplitude ratio A/D=0.8, and the wake shedding mode changes around A/D=0.8 from "P+S" to "2P" (P represents a pair of vortex shedding with opposite rotation directions, and S represents a single vortex shedding). In the vortex-induced vibration experiment of a single cylinder, the maximum amplitude when "lock-in" occurs is around 0.8D. ConclusionsThe amplitude ratio corresponding to the "zero lift coefficient" of the Cl-A/D model of forced vibrating cylinder under sub-critical Reynolds number is consistent with the maximum response amplitude ratio of the cylinder under vortex-induced vibration, and the shedding mode of the wake vortex changes under this amplitude ratio.