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Abstract Flapping insect wings collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect's ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the reaction moments, angular impulse, and peak stresses experienced by the wing during a collision. When evaluated over the duration of an external load, we found that buckling could reduce reaction moments and angular impulse up to 82% and 99%, respectively, compared to a homogeneous wing. This suggests the costal break can enhance flight stability. On the other hand, buckling maximally increased peak stresses two times compared to a homogeneous wing, indicating the costal break does not reduce likelihood of damage under the simplified loading considered. 

Abstract Flapping insect wings frequently collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect’s ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the peak stresses and reaction moments experienced by the wing during a collision. We found that costal break increased the wing’s natural frequency by about 50% compared to a homogeneous wing and thus reduced the stress associated with normal flapping. Buckling did not significantly affect peak stresses during collision. Joint buckling reduced the peak reaction moment by about 32%, suggesting that the costal break enhances flight stability. 

Abstract Flapping wings deform under both aerodynamic and inertial forces. However, many flapping wing fluid–structure interaction (FSI) models require significant computational resources which limit their effectiveness for high-dimensional parametric studies. Here, we present a simple bilaterally coupled FSI model for a wing subject to single-degree-of-freedom (SDOF) flapping. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. To verify the model experimentally, we construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum. Overall, the derived model estimates wing strain with good accuracy. In-vacuum, the wing has a large 3ω response when flapping at approximately one-third of its natural frequency due to a superharmonic resonance, where the superharmonic occurs due to the interaction of inertial forces and time-varying centrifugal softening. In-air, this 3ω response is attenuated significantly as a result of aerodynamic damping, whereas the primary ω response is increased due to aerodynamic loading. These results highlight the importance of (1) bilateral coupling between the fluid and structure, since unilaterally coupled approaches do not adequately describe deformation-induced aerodynamic damping and (2) time-varying stiffness, which generates superharmonics of the flapping frequency in the wing’s dynamic response. The simple SDOF model and experimental study presented in this work demonstrate the potential for a reduced-order FSI model that considers both bilateral fluid–structure coupling and realistic multi-degrees-of-freedom flapping kinematics moving forward. 

Fluid–structure interaction (FSI) plays a significant role in the deformation of flapping insect wings. However, many current FSI models are high-order and rely on direct computational methods, thereby limiting parametric studies as well as insights into the physics governing wing dynamics. We develop a novel flapping wing FSI framework that accommodates general wing geometry and fluid loading. We use this framework to study the unilaterally coupled FSI of an idealized hawkmoth forewing considering two fluid models: Reynolds-averaged Navier–Stokes computational fluid dynamics (RANS CFD) and blade element theory (BET). We first compare aerodynamic modal forces estimated by the low-order BET model to those calculated via high fidelity RANS CFD. We find that for realistic flapping kinematics, BET estimates modal forces five orders of magnitude faster than CFD within reasonable accuracy. Over the range flapping kinematics considered, BET and CFD estimated modal forces vary maximally by 350% in magnitude and approximately π/2 radians in phase. The large reduction in computational time offered by BET facilitates high-dimensional parametric design of flapping-wing-based technologies. Next, we compare the contributions of aerodynamic and inertial forces to wing deformation. Under the unilateral coupling assumption, aerodynamic and inertial-elastic forces are on the same order of magnitude—however, inertial-elastic forces primarily excite the wing’s bending mode whereas aerodynamic forces primarily excite the wing’s torsional mode. This suggests that, via conscientious sensor placement and orientation, biological wings may be able to sense independently inertial and aerodynamic forces. 

Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.