Modal Dynamics of Plunging Tapered Hydrofoils

Many aquatic animals and flying insects rely on flapping appendages for locomotion. The flexibility inherent in these appendages, seen in both fish fins and insect wings, has been correlated with increased efficiency and thrust. The flexural rigidity within these structures is commonly nonuniform and varies along the chord, with the leading edge being stiffer than the trailing edge. This variation in stiffness significantly influences the deformation behavior of the wing or fin, resulting in the propagation of traveling waves along the structure, which is linked to the performance of these animals. This study aims to further understand the relationships between the traveling wave dynamics of flexible foils with taper along the chord (varied geometrical stiffness) as a response to imposed motion profiles, and the output thrust. In this work, rectangular foils undergo a sinusoidal heaving motion with varied amplitude and frequency. Modal analysis is performed using a scanning laser vibrometer to measure resonant frequencies and 2D mode shapes of the foils in quiescent water as the imposed amplitude is varied. The complex indicator function is used to quantify the deformation behavior of the foils as standing or traveling waves at each amplitude. Particle image velocimetry is used to quantify the thrust from the wake of the foils.