Vortex-induced vibrations of an elliptic cylinder of low mass ratio: Identification of new response branches

Abstract

The classical resonance branches that construct the response of a freely vibrating circular or elliptic cylinder at low Reynolds numbers, Re, are "initial" and "lower." The existence of additional response branches, if any at low Re via alteration of controlling parameters, is unavailable in the literature. In this computational work, relating to a low mass ratio (m* = 1) and zero damping, i.e., m*ζ = 0 transverse-only vortex-induced vibrations of an elliptic cylinder over Re = 50-180, four response branches that are unreported in the literature are identified. The lock-in at such a low mass ratio is non-classical, and the new response branches are resolved close to the lock-in boundaries. These additional branches are designated as extended initial branch, extended lower branch, terminal branch, and quasi-periodic desynchronization branch. The method proposed by Kumar et al. ["Identification of response branches for oscillators with curved and straight contours executing VIV," Ocean Eng. 164, 616-627 (2018b)] has been employed to identify the branches by locating the Re region concerning the change of slope and discontinuous jumps of oscillation frequency. It is further shown that branching at a low mass ratio depends on structural damping, oscillator shape, and degree-of-freedom.