The relationship between resonance, thrust, and hydrodynamic efficiency of a torsional-spring-based passive pitching propulsor

In this work, the resonance phenomenon of a torsional-spring-based passive pitching propulsor is numerically investigated which aims to clarify the relationship among resonance, thrust, and hydrodynamic efficiency. The resonance is induced by varying both actuating frequency and torsional stiffness. Results show that resonance could enhance propulsive performance whether by boosting its thrust or enhancing its hydrodynamic efficiency depending on which variable it is relative to. When relative to torsional stiffness, resonance brings the maximum cycle-averaged thrust, whereas when relative to actuating frequency, resonance leads to the highest hydrodynamic efficiency. The performance difference is discussed, and the mechanisms for the enhancement of propulsive performance in resonance are analyzed. Meanwhile, a method for quickly calculating the resonance frequency of a propulsor with a given torsional stiffness is verified through our simulations. The study improves the understanding of the optimal performance of bio-inspired torsional-spring-based propulsors that utilize the resonance phenomenon and may advance the design of high-performance bio-inspired underwater vehicles.