In this study, we represent transient and unsteady dynamics of a cylinder undergoing vortex-induced vibration, by employing measurements of the fluid forces for a body controlled to vibrate sinusoidally, transverse to a free stream. We generate very high-resolution contour plots of fluid force in the plane of normalized amplitude and wavelength of controlled oscillation. These contours have been used with an equation of motion to predict the steady-state response of an elastically mounted body. The principal motivation with the present study is to extend this approach to the case where a freely vibrating cylinder exhibits transient or unsteady vibration, through the use of a simple quasi-steady model. In the model, we use equations which define how the amplitude and frequency will change in time, although the instantaneous forces are taken to be those measured under steady-state conditions (the quasi-steady approximation), employing our high-resolution contour plots.The resolution of our force contours has enabled us to define mode regime boundaries with precision, in the amplitude–wavelength plane. Across these mode boundaries, there are discontinuous changes in the fluid force measurements. Predictions of free vibration on either side of the boundaries yield distinct response branches. Using the quasi-steady model, we are able to characterize the nature of the transition which occurs between the upper and lower amplitude response branches. This regime of vibration is of practical significance as it represents conditions under which peak resonant response is found in these systems. For higher mass ratios (m* > 10), our approach predicts that there will be an intermittent switching between branches, as the vortex-formation mode switches between the classical 2P mode and a ‘2POVERLAP’ mode. Interestingly, for low mass ratios (m* ~ 1), there exists a whole regime of normalized flow velocities, where steady-state vibration cannot occur. However, if one employs the quasi-steady model, we discover that the cylinder can indeed oscillate, but only with non-periodic fluctuations in amplitude and frequency. The character of the amplitude response from the model is close to what is found in free vibration experiments. For very low mass ratios (m* < 0.36 in this study), this regime of unsteady vibration response will extend all the way to infinite normalized velocity.
Transient and steady‐state modelling of healthy and eccentric induction motors considering the main and third harmonic saturation factors