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The study of forced and free vibration of a cylinder has long been isolated. The internal relationship between free vibration and forced vibration has rarely been investigated. In this paper, the relationship between the forced and free vibration of a cylinder was established. A series of numerical simulations of a cylinder undergoing forced oscillations at a wide range of vibration amplitudes and frequencies were carried out, with the flow solver viv-FOAM-SJTU developed based on the open-source platform OpenFOAM. Complex demodulation analysis was conducted to quantify the spatial-temporal phase relationship between the forces and the displacement of the cylinder. It was found that, at some particular oscillating amplitudes and frequencies, the phase angle switched between positive and negative values, which corresponds to a vortex mode transferring from the 2P mode to the  2 P O mode. This distinct new mode “ 2 P O ” was closely related to the intermittent jumping between lower and upper branches of the amplitude responses of VIV. A prediction model was developed to obtain the VIV amplitude responses based on the numerical results of forced oscillation. The prediction results of three points located separately in the initial, upper, and lower branches of VIV agreed well with experimental measurements of an elastically mounted cylinder. This prediction model was thus expected to be suitable for predicting the response of VIV.

Prediction of the VIV Responses Based on the Numerical Solutions of Controlled Motion