This paper presents a study of the flow past elastically mounted cylinders with prescribed rotational oscillation about the cylinder centre, which are free to heave, or oscillate transverse to the flow. The configuration serves as an idealized model of a flapping-foil energy harvester. A range of geometries are tested, from the circular cylinder with an aspect ratio of 1.0 to elliptical cylinders up to aspect ratio of 6.0 approaching a flat plate. The driving frequency of the rotational oscillation is varied, while the amplitude of rotation is fixed at π/2, meaning both axes of the geometries present fully to the oncoming flow each cycle. The Reynolds number is 200. The natural frequency of the elastic-mounting is set to the Strouhal frequency for a circular cylinder. The ratio of the mass of the cylinder to the mass of the equivalent volume of displaced fluid is set to 5.0. Configurations with zero-damping reveal a rich parameter space, with increasing cross-stream oscillation with increasing geometry aspect ratio. Driving frequencies for peak oscillation amplitude are grouped around a driving frequency of 0.9 times the natural frequency of the elastic structure. The variation of the power input to actuate the rotational oscillation of the cylinder is also analysed. The fluid structure interaction is analysed for energy harvesting potential; power output is modelled by linear damping on the heave. Increasing the damping on the structure leads to optimal values of driving frequency and damping for each aspect ratio tested. For each aspect ratio, comparisons are drawn and similarities found between these optimal cases for power output and the undamped cases for maximum oscillation amplitude and velocity. The study of the parameter space serves as a useful starting point for further study of the many parameters affecting the performance of flapping-foil energy harvesting.