Lock-in in forced vibration of a circular cylinder

The phenomenon of lock-in/synchronization in uniform flow past an oscillating cylinder is investigated via a stabilized finite element method at Re = 100. Computations are carried out for various amplitudes and frequencies of cylinder oscillation to accurately obtain the boundary of the lock-in regime. Results from earlier studies show a significant scatter in the lock-in boundary. The scatter might be an outcome of the difference in data collection or the use of a different criterion for identifying lock-in. A new criterion for lock-in is proposed, wherein the following two conditions are to be satisfied. (i) The most dominant frequency in the power spectrum of lift coefficient matches the frequency of cylinder oscillation (fy) and (ii) other peaks in the power spectrum, if any, are present only at super-harmonics of fy. Utilizing this criterion, three flow regimes are identified on the frequency-amplitude plane: lock-in, transition, and no lock-in. The behaviour of the wake is also investigated by examining the power spectra of the velocity traces at various locations downstream of the cylinder. Wake-lock-in is observed during lock-in. A wake-transition regime is identified wherein the near wake, up to a certain streamwise location, is in a lock-in state while the downstream region is in a desynchronized state. For a fixed fy, the location beyond which the wake is desynchronized moves downstream as the amplitude of oscillation is increased. The proposed criterion for lock-in addresses the wide scatter in the boundary of the lock-in regime among earlier studies. Energy transfer from the fluid to the structure, per cycle of cylinder oscillation, is computed from the data for forced vibration. The data is utilized to generate iso-energy transfer contours in the frequency-amplitude plane. The free vibration response with zero structural damping is found to be in very good agreement with the contour corresponding to zero energy transfer.