Synchronization Study on Vortex-Induced Vibrations Using Wake Oscillator Model

Vortex-Induced Vibration (VIV) is often modelled as a two-way-coupled phenomenon wherein the structure and the wake behave as two interacting oscillators. In this chapter, we analyse the coupled interactions between these two oscillators from the purview of synchronization theory. To that end, a low-order wake oscillator model comprising of a classical Van der Pol (VDP) oscillator, describing the wake dynamics, and a single degree-of-freedom structural oscillator is considered. Frequency and phase synchronization of this fluid-elastic system are characterized by evaluating the relative mean frequency and phase-locking values (PLV), respectively. The measures are evaluated adopting Hilbert-transform-based analytic signal approach. The synchronization behaviour of a linear and a non-linear structural oscillator with cubic stiffness is compared. Although the linear structure shows a phase-synchronized response throughout the range of flow speed considered in this chapter, an interesting asynchronous region prior to lock-in is identified for the non-linear structure. This is further investigated for different non-linearity coefficients in the structural oscillator.