Evolutionary optimization of the flexibility and gait for a self-propelled bio-inspired propulsor

Many animals propel themselves through the water with sinusoidal, continuous gaits while some others adopt an intermittent and/or a non-sinusoidal gait. Additionally, animal propulsors can range in their flexibility from highly flexible to very stiff. Here, we examine the interplay between the flexibility of a propulsor and its gait. To probe this interplay, an evolutionary algorithm coupled with a two-dimensional boundary element method numerical framework is used to solve the multi-objective optimization problem where both the non-dimensional speed and range of a self-propelled swimmer are maximized. The hydrofoil is forced in a periodic pitching motion about its leading edge where the shape and the intermittency of the gait are varied by using Jacobi elliptic functions and burst-and-coast swimming, respectively. A lumped flexibility model in the form of a torsional spring is located at the mid-chord to model chordwise flexibility in the hydrofoil where the non-dimensional flexibility is altered by varying the spring stiffness. The results are presented in a novel performance map, which examines the interplay between the efficiency, the swimming speed, and the range of swimmer. The associated wake dynamics are also discussed.