A general formulation for the fluid–structure interaction of an airfoil undergoing prescribed pitching and passive heave and deformation about an arbitrary axis is given in the linearized potential flow limit. The resulting three algebraic equations provide the heave and deformation amplitudes linearly from two of the equations, as well as the torque that generates the pitching motion (and hence the input power) from the third. Both, the energy harvesting and the propulsion problems are analyzed. In the first case, energy is harvested at the pivot point through dampers so that the efficiency is obtained once the heaving motion and the input power are computed. In the second problem, the prescribed pitch and the computed heave and deformation yield the thrust as well as the propulsive efficiency with the obtained input power. The present analytical results allow for a general survey of these two physical problems as the multiple governing parameters are varied. It is generally found that the best performance is achieved around the first natural frequency, which is obtained here from a simple algebraic expression. The formulation is validated with previous experimental and numerical results. The effect of flexibility maximizing the energy harvesting efficiency is particularly analyzed.

在线性化势流极限中给出了翼型的流固耦合的一般公式，该翼型经历了规定的俯仰和被动升沉以及绕任意轴的变形。由此产生的三个代数方程从两个方程中线性地提供升沉和变形幅度，以及从第三个方程中产生俯仰运动的扭矩（以及输入功率）。分析了能量收集和推进问题。在第一种情况下，通过阻尼器在枢轴点收集能量，以便在计算出升沉运动和输入功率后获得效率。在第二个问题中，规定的螺距和计算的升沉和变形产生推力以及获得的输入功率的推进效率。由于多个控制参数不同，目前的分析结果允许对这两个物理问题进行一般调查。通常发现最好的性能是在第一个自然频率附近实现的，这里是从一个简单的代数表达式中获得的。该公式已通过先前的实验和数值结果进行验证。特别分析了最大化能量收集效率的灵活性的影响。