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

A nonlinear theory for a flexible unsteady wing

This paper extends the previous studies by Wu [Wu TY (2001) Adv Appl Mech 38:291–353; Wu TY (2005) Advances in engineering mechanics—reflections and outlooks. World Scientific; Wu TY (2006) Struct Control Health Monit 13:553–560] to present a fully nonlinear theory for the evaluation of the unsteady flow generated by a two-dimensional flexible lifting surface moving in an arbitrary manner through an incompressible and inviscid fluid for modeling bird/insect flight and fish swimming. The original physical concept founded by Theodore von Kármán and William R. Sears [von Kármán T, Sears WR (1938) J Aero Sci 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 extended to a fully nonlinear consideration. The new theory employs a joint Eulerian and Lagrangian description of the wing motion to establish a fully nonlinear theory for a flexible wing moving with arbitrary variations in wing shape and trajectory, and obtain a fully nonlinear integral equation for the wake vorticity in generalizing Herbert Wagner’s [Wagner H (1925) ZAMM 5:17–35] linear version for an efficient determination of exact solutions in general

A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate

In this paper, we introduce a three-dimensional numerical method for computing the wake behind a flat plate advancing perpendicular to the flow. Our numerical method is inspired by the panel method of J. Katz and A. Plotkin [J. Katz and A. Plotkin, Low-speed Aerodynamics, 2001] and the 2D vortex blob method of Krasny [R. Krasny, Lectures in Appl. Math., 28 (1991), pp. 385--402]. The accuracy of the method will be demonstrated by comparing the 3D computation at the center section of a very high aspect ratio plate with the corresponding two-dimensional computation. Furthermore, we compare the numerical results obtained by our 3D numerical method with the corresponding experimental results obtained recently by Ringuette [M. J. Ringuette, Ph.D. Thesis, 2004] in the towing tank. Our numerical results are shown to be in excellent agreement with the experimental results up to the so-called formation time

Comments and corrections on 3D modeling studies of locomotor muscle moment arms in archosaurs

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A nonlinear theory for a flexible unsteady wing

This paper extends the previous studies by Wu [Wu TY (2001) Adv Appl Mech 38:291–353; Wu TY (2005) Advances in engineering mechanics—reflections and outlooks. World Scientific; Wu TY (2006) Struct Control Health Monit 13:553–560] to present a fully nonlinear theory for the evaluation of the unsteady flow generated by a two-dimensional flexible lifting surface moving in an arbitrary manner through an incompressible and inviscid fluid for modeling bird/insect flight and fish swimming. The original physical concept founded by Theodore von Kármán and William R. Sears [von Kármán T, Sears WR (1938) J Aero Sci 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 extended to a fully nonlinear consideration. The new theory employs a joint Eulerian and Lagrangian description of the wing motion to establish a fully nonlinear theory for a flexible wing moving with arbitrary variations in wing shape and trajectory, and obtain a fully nonlinear integral equation for the wake vorticity in generalizing Herbert Wagner’s [Wagner H (1925) ZAMM 5:17–35] linear version for an efficient determination of exact solutions in general

Research issues in biological inspired flying robots

Biological inspired locomotion robotics is an area reveal-ing an increasing research and development. In spite of all the recent engineering advances, robots lack capabilities with respect to agility, adaptability, intelligent sensing, fault-tolerance, stealth, and utilization of in-situ power resources compared to some of the simplest biological organisms. The general premise of bio-inspired engineer-ing is to distill the principles incorporated in successful, nature-tested mechanisms, capturing the biomechatronic designs and minimalist operation principles from nature’s success strategies. Based on these concepts, several robots that adopt the same locomotion principles as animals, like legs for walking, fins for swimming, segmented body for creeping and peristaltic movements for worm like loco-motion, were developed in the last years. Recently, flap-ping wings robots are also stating to make their debut but there are several problems that need to be solved before they may fly autonomously. This paper analyses the ma-jor developments in this area and the directions towards future research.N/

Using Computational and Mechanical Models to Study Animal Locomotion

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.