The fluid-structure interaction in a foil undergoing prescribed heave with passive pitching and flexibility about any pivot is formulated in the linear inviscid limit using a quartic approximation for the deflection. The resulting system of three algebraic equations is valid for arbitrary mass and stiffness distributions of the foil. The small pitching and deformation amplitudes result linearly from two of the equations, while the third equation provides the force at the pivot point that generates the heaving motion, and hence the power input. This general formulation allows to analyze jointly both the propulsion and the energy harvesting problems for this class of flapping foils. In the first case, the thrust force is readily obtained from the prescribed heave and the resulting pitching and deformation, and consequently the propulsive efficiency once the power input is computed. In the second problem, the energy may be harvested by linear and/or torsional dampers at the pivot point, so that the efficiency of the system is readily computed once the pitch motion and the power input are obtained. Thus, the present work allows for a depth parametric survey and analysis of these two physical problems. The best performance is usually obtained around the first natural frequency of the fluid-structure system, which is obtained here by minimizing an algebraic function. The formulation is validated by reproducing some previous results for both problems, most of them obtained numerically for rigid foils and without the simplicity nor the richness in the parameter space of the present formulation. The parametric range for which flexibility maximizes the propulsion and the energy harvesting efficiencies in relation to an otherwise identical rigid-foil system is analyzed. (C) 2021 Elsevier Ltd. All rights reserved.
