Identification of response branches for oscillators with curved and straight contours executing VIV

Abstract

For oscillators with curved contours, variation of cylinder amplitude with Reynolds number or reduced speed is adequate to accurately identify the extent of resonance branches and critical points marking the transition from one branch to another. However, in presence of straight edges in body contour, the response curve at certain locations of transition, exhibits smooth variation. The same is seen with smooth contoured oscillators of low mass ratio, i.e. value of mass ratio being close to unity. The frequency curves, in contrast, reflect all the transitions that are not captured in the response variation. A simple method is proposed to accurately predict the branching and associated transition points with the aid of oscillation and shedding frequency curves. It is noted that the frequency profile undergoes a change of slope at the location of a transition. Using the proposed method, branching is analyzed for elliptic, square and truncated circular cylinders of mass ratio 10, each of them executing undamped vortex-induced vibrations (VIV) at low Reynolds numbers (=60-150) simultaneously along and across the flow. Illustrations are extended for a square cylinder of mass ratio 1, too. For the first time, VIV results are presented for a truncated circular cylinder.