Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder's equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.