# Natural frequency effect on the path of an elastically supported circular cylinder

## Description

Flow around a freely vibrating circular cylinder in two-degrees-of-freedom is investigated at low Reynolds numbers using two-dimensional numerical simulation. Systematic computations are carried out to investigate the effect of cylinder’s natural frequency fN on the oscillation amplitudes and aerodynamic force coefficients. The mass ratio and the structural damping coefficient values are fixed at m*=10 and ζ=0, respectively. In addition to the typical distorted figure-eight motion, a raindrop-shaped path is also found whose range widens with increasing fN. Within this range the streamwise cylinder oscillation amplitude reaches higher values compared to figure-eight motions and the curves shift upwards with increasing fN. Sudden switches in the vortex structure occur near the upper boundaries separating the raindrop-shaped and distorted figure-eight motion domains. The root-mean-square (rms) values of lift plotted against U*St0 shift upwards in the raindrop-shaped motion range and downwards in the figure-eight motion range, while the rms of drag shifts to higher values in both regimes with increasing fN. The time-mean of lift coefficient jumps abruptly between two solutions. Using pre- and post-jump analysis it is shown that these solutions are mirror images of each other. Chaotic cylinder paths are observed when increasing the natural frequency over a critical value.