Mechanical resonance conditions in insect flapping wing apparatus: insights from flight and swimming of a miniature wasp Tiphodytes gerriphagus

Evidence suggests that insects may utilize resonant mechanics during flight to optimize energetic effciency, though whether this mechanism is universal across all insect species remains debated. Microinsects appear particularly intriguing in this context: they exhibit agility comparable to larger species despite experiencing higher aerodynamic damping forces on their wings. We investigated mechanical resonance dynamics focusing on the miniature wasp Tiphodytes gerriphagus -- a remarkable species capable of both aerial flight and underwater locomotion, using wings in both cases. This dual-mode mobility introduces additional biomechanical constraints that simplify parameter identification in the analysis. We developed a reduced-order model incorporating muscle activation, internal inertial and viscous damping forces, thoracic elasticity, and inertial and fluid-dynamic forces acting on the wing. This model represents the insect flight apparatus as a one-dimensional oscillator. It employs capillary analogy modeling, integrated with a wing-thorax-muscle system undergoing periodic flapping motions. Our results demonstrate limited flight motor resonance potential in air, caused by strong damping effects, and unavoidably overdamped conditions underwater.