Vibration and sound of a flapping airfoil: The limit of small bending rigidity

We investigate the near and far fields of a thin elastic airfoil set at uniform low-Mach flow and subject to leading-edge heaving actuation. The airfoil is “hanged” in the vertical direction and is free at its downstream end, so that “hanging chain” gravity-induced tension forces apply. The structure bending rigidity is assumed small, and we focus on analyzing the differences between a highly elastic airfoil and a membrane (where the bending rigidity vanishes). The near field is studied based on potential thin airfoil theory, whereas the acoustic field is investigated using the Powell-Howe acoustic analogy. The results shed light on the specific effect of structure bending stiffness on the dynamics and acoustic disturbance of an airfoil.