Bending Modes and Fluid–Structure Interaction in Fish-Inspired Swimmers: Implications for Flexible Underwater Robot Design

Body flexibility plays a crucial role in the interaction between swimming fish and its surrounding fluid. This study investigates the hydroelastic response of passive fish-like bodies with steady forward motion. Hydrodynamic loads are modeled using slender-body theory while internal forces and structural dynamics are represented by Euler-Bernoulli beam theory. A finite-element formulation was developed to determine the wet bending modes as a function of body geometry, stiffness and forward speed. The analysis found that primary modes correspond closely to the kinematic patterns observed in fish locomotion and were consistent with Strouhal numbers for efficient propulsion. It revealed how biological systems by increasing their effective body stiffness via muscle contraction can maintain similar deformation pattern and Strouhal number while raising tail-beat frequency and forward speed. A parametric scaling analysis further indicate that the relationship between swimming frequency and velocity observed across aquatic animals can be explained by the scaling of structural modes of the body. The results support the hypothesis that mechanical resonance plays an important role in swimming performance and highlight the interplay between body size, flexibility, and operating regime on the hydroelastic response. These findings provide physical insight that may guide the design of flexible fish-inspired underwater robots.