Relationship between wake and cylinder dynamics for a cylinder undergoing modulated vortex-induced vibrations

Vortex-induced vibrations (VIV) in the initial branch are investigated for a 2-degree-of-freedom circular cylinder placed near a plane boundary ( Re = UD/nu = 200 , where U is the inflow average streamwise velocity, D is the cylinder diameter, and nu is the kinematic viscosity) with imposed sinusoidal perturbations of the free stream at resonant, 2 f(o), and near-resonant conditions, 2.2 f(o) (f(o) is the natural shedding frequency). The cylinder exhibits a quasi-periodic response, which challenges the comprehension of its relationship with the wake dynamics obtained through conventional VIV models. The total force acting on the cylinder is decomposed into a vortex-induced force, F-V, linearly coupled to VIV, and a force induced by the effective mass of the cylinder, F-S, which is non-linearly coupled to VIV. The proposed semi-empirical model reveals that the time-varying nature of the effective mass in F-S drives the non-linear response. The model's physical consistency is verified against simulation results. While focusing on VIV in the initial branch, the validity of the proposed model is expected to extend to other branches of response, offering a promising avenue for developing a robust predictive model for VIV under various flow conditions.