Fluid-structure interaction in compliant insect wings.

Insect wings deform significantly during flight. As a result, wings act as aeroelastic structures wherein both the driving motion of the structure and the aerodynamic loading of the surrounding fluid potentially interact to modify wing shape. We explore two key issues associated with the design of compliant wings: over a range of driving frequencies and phases of pitch-heave actuation, how does wing stiffness influence (1) the lift and thrust generated and (2) the relative importance of fluid loading on the shape of the wing? In order to examine a wide range of parameters relevant to insect flight, we develop a computationally efficient, two-dimensional model that couples point vortex methods for fluid force computations with structural finite element methods to model the fluid-structure interaction of a wing in air. We vary the actuation frequency, phase of actuation, and flexural stiffness over a range that encompasses values measured for a number of insect taxa (10-90 Hz; 0-π rad; 10(-7)-10(-5) N m(2)). We show that the coefficients of lift and thrust are maximized at the first and second structural resonant frequencies of the system. We also show that even in regions of structural resonance, fluid loading never contributes more than 20% to the development of flight forces.