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-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.