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*zeta), or a high mass- damping thigh m*zeta). For our low m*zeta, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lo wer branch. For the classical Feng-type response, at high m*zeta, there exi st only two response branches, namely the initial and lower branches. The p eak amplitude of these vibrating systems is principally dependent on the ma ss-damping (m*zeta), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the mass ratio, m*. At low (m*zeta), the transition between initial and upper response branches invol ves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper-lower branches. A 180 degrees jump in phase angle phi is found only when the flow jumps between the upper-lower branches of response. The good collapse of p eak-amplitude data, over a wide range of mass ratios (m* = 1-20), when plot ted against (m* + C-A)zeta in the "Griffin" plot, demonstrates that the use of a combined parameter is valid down to at least (m* + C-A)zeta similar t o 0.006. This is two orders of magnitude below the "limit" that had previou sly been stipulated in the literature, (m* + C-A)zeta > 0.4. Using the actu al oscillating frequency (f) rather than the still-water natural frequency (f(N)), to form a normalized velocity (U*/f*), also called "true" reduced v elocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratios m*. Such a co llapse of response plots cannot be predicted a priori, and appears to be th e first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson-Roshko (Williamson & R oshko 1988) map of vortex wake patterns from forced vibration studies. Visu alization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with t he 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluct uating forces on the body, which is not unexpected. It is possible to simpl y estimate the lift force and phase using the displacement amplitude and fr equency. This approach is reasonable only for very low m*. (C) 1999 Academi c Press.