Reduced-order modeling and experimental studies of bilaterally coupled fluid- structure interaction in single- degree-of-freedom flapping wings

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-offreedom (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. Invacuum, 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. Inair, 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-degreesof- freedom flapping kinematics moving forward.