The effect of cubic stiffness nonlinearity on the vortex-induced vibration of a circular cylinder at low Reynolds numbers

The vortex-induced vibration (VIV) of a circular cylinder elastically supported by linear and cubic springs is investigated numerically at low Reynolds numbers. The cylinder has a low mass ratio and zero structural damping. Nine dimensionless cubic stiffness nonlinearity strength values are considered. It is found that within the parameter space examined, the VIV response for the linear and softening springs can be divided into four regimes, namely the initial, upper, lower and desynchronised regimes. When the softening spring nonlinearity gets stronger, there exist a reduction in the peak amplitude and shifts in the initial-upper branch and upper-lower branch transitions to lower Reynolds number ranges. In contrast, as the hardening spring nonlinearity increases, the response envelope moves to a higher Reynolds number range and the profile of the initial and upper branches becomes smoother with the lower branch gradually disappearing. In the hardening spring case, the beating response is observed near the low end of the initial branch up to the high end of the initial branch. The modulations in the vibration amplitude gradually diminish with increasing Reynolds number. The cubic spring results coincide with those of the linear spring when they are presented with the equivalent reduced velocity. Due to the low Reynolds number range considered, the majority of the vortex shedding is in the 2S mode. The wake in the cases with smaller vibration amplitudes exhibits a single-row configuration. Whereas, a double-row vortex street is mainly observed in the upper branch. Disorders in the wake are found to be associated with beating responses which have larger vibration amplitudes