On the relationship between wake and cylinder dynamics for quasi-periodic vortex-induced vibrations*

The weakly nonlinear response of a forced self-sustained oscillator for vortex-induced vibrations (VIV) in the initial branch is investigated for a 2D cylinder near a plane boundary in a uniform flow (Re=200) perturbed sinusoidally at resonant, 2f_o, and near-resonant conditions, 2.2f_o (f_o is the natural shedding frequency). The cylinder exhibits a quasi-periodic response and its underlying physics are not captured using common VIV models. The total force acting on the cylinder is decomposed into a vortex-induced force, F_v(t), and a force induced by effective mass, F_s(t). Fv(t) is linearly coupled to the cylinder's motion, while F_s(t) serves as a nonlinear coupling mechanism. A semi-empirical model is proposed, showing that the time-varying nature of the effective mass in F_s(t) drives the nonlinear response. This model elucidates the physics underlying quasi-periodic VIV and explains observed frequency drift and crosstalk. This model represents a non-isochronous oscillator, exhibiting four branches of response and two lock-on regimes similar to what is observed for VIV. Hence, it shows promise as a predictive tool for VIV response under various flow conditions.