Critical mass in vortex-induced vibration of a cylinder

In this paper, we study the transverse vortex-induced vibrations of a cylinder at low mass-damping values. The response in this case consists of three distinct branches; namely the initial, upper and lower branches. For an elastically-mounted cylinder, the oscillation frequency can,be shown to be primarily dependent on the mass ratio (m* = mass/displaced fluid mass). For large mass ratios, m* = O(100), the vibration frequency for synchronization lies close to the natural frequency (f* = f/f(N) similar to 1.0), but as mass is reduced to m* = O(1), f* can reach remarkably large values. We deduce an expression for the frequency of the lower-branch vibration, at small mass-damping values, as follows: f(lower)(*) = rootm* + 1/m* - 0.54 which agrees very well with a wide set of experimental data. This frequency equation indicates the existence of a critical mass ratio, where the frequency f* becomes large: m(crit)(*) = 0.54. When m* < m(crit)(*), it can be shown that the lower branch can never be reached and ceases to exist. In this case, the upper branch regime of synchronisation is predicted to continue to infinite normalized flow speed, U* --> infinity, where U* = U/f(N)D is the conventionally used normalized flow speed. In the case of a cylinder with no structural restoring force, the natural frequency f(N) is zero, and therefore the conventionally defined U* is infinite. Experiments under these conditions indicate that there are negligible oscillations as mass ratio is reduced from large values to m* of the order of unity. However, a further reduction in mass exhibits a surprising result; large-amplitude oscillations suddenly appear for values of mass less than a critical mass ratio,of 0.542. This result for the critical mass from experiments with a cylinder having no structural restoring force is in remarkable agreement with the earlier predictions from the elastically-mounted cylinder experiments. (C) 2003 Elsevier SAS. All rights reserved.