Optimal chordwise stiffness distribution for self-propelled heaving flexible plates

The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness K̃ is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same K̃, the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal K̃ at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific K̃ in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.