Abstract This work investigates the flow-induced motion originating from the classical-flutter instability, and it is motivated by energy-harvesting applications. The influence of several sets of dynamic parameters is studied, improving the scientific understanding of the large-amplitude response and guiding the design of more unstable configurations. Wind-tunnel tests were conducted on elastically-suspended rigid models with an elongated rectangular cross section, undergoing a two-degree-of-freedom motion with transverse (heaving) and rotational (pitching) components. The aeroelastic setup was specifically developed to allow for a large-amplitude motion (about one chord in heaving and more than 90°in pitching) and to simulate an energy-conversion apparatus by increasing the heaving damping (up to about 18% of the critical one) through eddy-current dampers. After a sub-critical bifurcation, large limit-cycle oscillations were recorded, with steady-state amplitudes increasing with the flow speed. For some configurations, a low-amplitude response was also observed around the instability threshold. It was found that a small mass unbalance aft of the elastic axis significantly fosters the system instability and affects the heaving and pitching motion amplitudes. The latter are also markedly influenced by the still-air frequency ratio. In the presence of high values of the heaving damping, the post-critical amplitude is usually reduced, although a destabilising effect of damping was observed in some specific cases. Finally, the motion is magnified for lower-inertia systems.