"We found that the simple up and down wavelike stroke of wings at the resonance frequency is easier to implement and generates lift comparable to winged insects that employ a significantly more complex stroke," said Alexander Alexeev, an assistant professor in Georgia Tech's School of Mechanical Engineering.
The 5 page paper is here. Physics Review E - Resonance of flexible flapping wings at low Reynolds number
Using three-dimensional computer simulations, we examine hovering aerodynamics of flexible planar wings oscillating at resonance. We model flexible wings as tilted elastic plates whose sinusoidal plunging motion is imposed at the plate root. Our simulations reveal that large-amplitude resonance oscillations of elastic wings drastically enhance aerodynamic lift and efficiency of low-Reynolds-number plunging. Driven by a simple sinusoidal stroke, flexible wings at resonance generate a hovering force comparable to that of small insects that employ a very efficient but much more complicated stroke kinematics. Our results indicate the feasibility of using flexible wings driven by a simple harmonic stroke for designing efficient microscale flying machines.
In summary, we used three-dimensional computational modeling to examine the hovering aerodynamics of flexible plunging wings at Re=100. Our simulations revealed that at resonance tilted elastic wings driven by a simple harmonic stroke generate lift comparable to that of small insects that employ a significantly more complex stroke. Such simple oscillations can be more readily adapted for designing flapping MAVs. Furthermore, we showed that just by changing wing elasticity, the lift force can be increased by two orders of magnitude indicating the drastic effect that elasticity may play in flapping flight. We found that elastic wings at resonance yield a high lift-to-weight ratio and efficiency. We identified two oscillation regimes leading to different wing bending modes that maximize the lift and efficiency, respectively. These two regimes take place at frequencies that differ by approximately 30%. Therefore, they can be dynamically changed by altering the flapping frequency. This could be useful for regulating the flight of flapping-wing MAVs since high lift is typically needed only during takeoff, while the improved aerodynamic efficiency is essential for a long-distance cruise flight.
Finally we note that in the present studies, we focused on the hovering flight with flexible wings at resonance. To employ the resonance flapping in practical MAV applications it will be necessary to examine how this approach can be adapted for thrust generation in forward flight and how the resonant wings behave and can be effectively controlled in different flow conditions including unsteady gusty environments. With respect to the former, a thrust force can be generated by using flapping wings with a nonzero angle of incidence. Furthermore, here we examined flexible wings with a fixed aspect ratio and uniform mechanical properties. Although these simple wings could be more readily manufactured, the use of wings with an optimized geometry, nonuniform structural and anisotropic mechanical properties, and asymmetric stroke kinematic may further enhance the resonance performance of flapping wings. These studies are currently underway.
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