Effects of natural frequency ratio on vortex-induced vibration of a circular cylinder in steady flow

This paper investigates the effects of the natural frequency ratio on the vibration response of an elastically mounted circular cylinder in fluid flows at a low Reynolds number of 200 and a mass ratio of 2. The natural frequency ratio (R-F) is defined as the ratio of natural frequency in the in-line direction to that in the cross-flow direction. Compared with previous studies, this paper extended the range of natural frequency ratios from 1-2 to 1-4 and found the most complex vibration and wake flow occur at natural frequency ratios of 2.5 and 3. Modes 2S (two single vortices), 2P (two pairs of vortices), and P+S (one pair and a single vortex) are defined as flow modes where two single vortices, two pairs of vortices, and one pair plus and one single vortices are shed from the cylinder in one period of vibration, respectively. The new findings for R-F = 2.5 and 3 include a new 2P mode that only exists when R-F = 2.5 and 3, a bi-stable wake mode where the wake flow could be either the 2P or the P+S mode, depending upon the initial condition, and, most interestingly, a tri-stable wake mode where the wake flow could be the 2P, P+S, or non-lock-in mode. In bi-stable and tri-stable regimes, once one wake flow mode is set, it does not change to other modes. In addition, the vibrations for a specific flow velocity but different modes may have different amplitudes, but their vibration frequencies are the same. The mode T wake flow is a flow mode where the flow switches between two modes alternately and the vibration has a beating feature. Three types of flow switching in mode T are found: 2S-1S switch, 2S-P+S switch, and 2S-2P switch. Mode 1S is a mode where two single vortices are shed in two vibration periods. It cannot exist itself and must co-exist with mode 2S. A 270 degrees -360 degrees phase between the displacements in the in-line and cross-flow directions suppresses the formation of the mode 2P wake, and a 0 degrees -45 degrees phase stimulates the mode 2P wake.