Meeting Abstract
Flapping insect wings deform under both inertial and aerodynamic forces. This fluid-structure interaction (FSI) is beneficial to aerodynamic performance and energetic efficiency. However, many flapping wing FSI models rely on direct numerical methods and require considerable computational resources to solve. Here, we present a simple, analytic FSI model for a wing subjected to single degree-of-freedom flapping that can be solved with minimal computational effort. The structural model is developed via the Lagrangian formulation and fluid loading is accounted for through a blade element approach that considers lift, drag and added mass forces. We validate this model experimentally by flapping a paper wing both in air and in vacuum using a custom rotation stage and recording strain at the base of the wing. Agreement between experimental measurements and model predictions is good. In vacuum, the wing experiences a superharmonic resonance when flapping at 1/3 its natural frequency due to periodic softening of this wing – this superharmonic response is attenuated in air due to fluid damping. We then use our model to study the influence of added mass when wing surface density is similar to that of a Manduca sexta wing. We show that, in addition to shifting the wing’s natural frequency, added mass increases fluid loading on the wing by approximately 15%. The increased loading cannot be accounted for by adjusting the wing’s natural frequency in simulation alone and must be treated as an independent forcing function. This work is an important first step towards developing FSI models that account for more realistic multiple degree-of-freedom flapping kinematics and complex wing geometries.
