Low-Order Aeroelastic Modeling of Flapping, Flexible Wings

Abstract

Flapping insect wings deform under aerodynamic and inertial-elastic loads. Existing aeroelastic wing models are computationally expensive, and consequently, the physics governing flexible wing deformation are not well understood. This paper develops a low-order, one-way coupled aeroelastic model of an arbitrary geometry wing undergoing three-dimensional rotation. The model is developed using the Lagrangian formulation and generalized aerodynamic loads are determined through a blade-element-momentum approach. The in-air and in-vacuum responses of a simulated Hawkmoth wing are compared for various conditions. During normal flight, simulation results show aerodynamic loading causes a 25% increase in maximum wingtip deflection versus a wing flapping in vacuum. This suggests aerodynamics plays a moderate role in structural deformation. Further parametric studies indicate (1) deviations in flap frequency excite torsional resonance and (2) the relative phase between pitch and roll rotations dramatically affects in-air wing response. Both the aeroelastic model and simulation results can guide optimal wing design for small-scale flapping wing micro air vehicles.