Higher resonances improve the swimming performance of flexible bio-inspired propulsors

This study establishes the role of higher resonant frequencies on the swimming performance of flexible bio-inspired propulsors. Biological and bio-inspired swimmers typically swim at or near their first resonance to achieve high efficiency and thrust. These swimmers also have higher resonances that could yield the same performance benefits; however, the role of these higher resonances is not well understood. This study experimentally identifies the thrust, kinematics, and power performance of flexible propulsors across resonances and uncovers the fluid-structural mechanism that governs the performance. We experimentally test multiple propulsors that share a simplified design consisting of a constant cross-section beam excited by piezoelectric actuators in quiescent water and with stiffnesses in the range of biological swimmers. Our results demonstrate that higher resonances significantly improve the performance compared to the fundamental resonance yielding a $2\times$ increase in thrust to power ratio, up to $11\times$ increase in absolute thrust, while requiring $<25\text{\%}$ of the displacement amplitude.

While the higher resonances yield better overall performance, we show that higher resonances are less effective at converting tail velocity into thrust since the thrust coefficient depends on the mode shape. We determine that higher resonances engage less fluid mass, and show that the effective aspect ratio (wavelength normalized by width) is a predictor of performance across resonances. These results indicate that higher resonances could be a viable swimming option to improve the thrust and efficiency of stiffer bodied swimmers while yielding smaller displacement amplitudes that improve operation near obstacles.