A nonlinear 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 Kármán 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.
Author preprint. Dedication: This work is dedicated in commemoration of Professor Thomas K. Caughey for his lifetime contributions of great significance to science, engineering, and engineering science, for his role model in truly outstanding scholarship, and for paying a sincere tribute to his most distinguished life and work. I am most appreciative for the gracious encouragement from Dr. Chinhua S. Wu and the American-Chinese Scholarship Foundation. Published version -- Copyright © 2005 John Wiley & Sons, Ltd. Structural Control and Health Monitoring Volume 13, Issue 1 (January 2006). Special Issue: Thomas K. Caughey Memorial Issue. Issue Edited by George W. Housner, James K. Knowles, Takuji Kobori, Sami F. Masri.