The effect of two degrees of freedom on vortex-induced vibration at low mass and damping

Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow ( $Y$ -motion), there are almost no papers on the more practical case of vortex-induced vibration in two degrees of freedom ( $X,Y$ motion) where the mass and natural frequencies are precisely the same in both $X$ - and $Y$ -directions. We have designed the present pendulum apparatus to achieve both of these criteria. Even down to the low mass ratios, where $m^*\,{=}\,6$ , it is remarkable that the freedom to oscillate in-line with the flow affects the transverse vibration surprisingly little. The same response branches, peak amplitudes, and vortex wake modes are found for both $Y$ -only and $X,Y$…