Motions, Forces and Mode Transitions in Vortex-Induced Vibrations at Low Mass-Damping

These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m*ζ), or a high mass-damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ ∼0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*.