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.

使用挠度的四次逼近，在线性无粘极限中公式化了箔片中经过预定起伏，被动俯仰和绕任何枢轴的挠性的流体-结构相互作用。三个代数方程的结果系统对于箔的任意质量和刚度分布都是有效的。较小的俯仰和变形幅度是由两个方程式线性得出的，而第三个方程式则在枢轴点提供了产生升沉运动的力，从而产生了动力输入。该通用公式允许共同分析此类拍打箔的推进和能量收集问题。在第一种情况下，推力很容易从规定的起伏以及由此产生的俯仰和变形中获得，因此，一旦计算出功率输入，便具有推进效率。在第二个问题中，能量可以通过枢轴上的线性和/或扭转阻尼器来收集，因此一旦获得俯仰运动和功率输入，就可以轻松计算系统的效率。因此，本工作允许对这两个物理问题进行深度参数调查和分析。通常，在流体结构系统的第一个固有频率附近可获得最佳性能，这是通过最小化代数函数获得的。通过针对两个问题再现一些先前的结果来验证该配方，其中大多数问题是通过数值获得的，用于刚性箔，并且没有本配方的简单性或参数空间的丰富性。