A non‐linear unsteady flexible wing theory

This paper extends a previous study by Wu ( Adv. Appl. Mech. 2001; 38 :291–353) to continue developing a fully non‐linear theory for calculation of unsteady flow generated by a two‐dimensional flexible lifting surface moving in arbitrary manner through an incompressible and inviscid fluid for modelling bird/insect flight and fish swimming. The original physical concept elucidated by von Ká rmá n and Sears ( J. Aeronau Sci. 1938; 5 :379–390) in describing the complete vortex system of a wing and its wake in non‐uniform motion for their linear theory is adapted and applied to a fully non‐linear consideration. The new theory employs a joint Eulerian and Lagrangian description of the lifting‐surface movement to facilitate the formulation. The present investigation presents further analysis for addressing arbitrary variations in wing shape and trajectory to achieve a non‐linear integral equation akin to Wagner's ( Z. Angew. Math. Mech. 1925; 5 :17–35) linear version for accurate computation of the entire system of vorticity distribution. Copyright © 2005 John Wiley & Sons, Ltd.