| Citation: | LIU Xin-jian, YUAN Tian-bao. Effects of Unsteady Deformation of a Flapping Wing on Its Aerodynamic Forces[J]. Applied Mathematics and Mechanics, 2008, 29(6): 663-675. | 
 
	                | [1] | Dickinson M H, Gtz K G.Unsteady aerodynamic performance of model wings at low Reynolds numbers[J].J Exp Biol,1993,174(1):45-64. | 
| [2] | Ellington C P, Van den Berg C.Willmott A P. Leading edge vortices in insect flight[J].Nature,1996,384(6610):626-630. doi:  10.1038/384626a0 | 
| [3] | Willmott A P, Ellington C P, Thomas A R.Flow visualization and unsteady aerodynamics in the flight of the hawkmoth, Manduca sexta[J].Philos Trans Roy Soc Lond,Ser B,1997,352(1351):303-316. doi:  10.1098/rstb.1997.0022 | 
| [4] | Liu H, Ellington C P, Kawachi K,et al.A computational fluid dynamic study of hawkmoth hovering[J].J Exp Biol,1998,201(4):461-477. | 
| [5] | Sun M, Tang J. Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion[J].J Exp Biol,2002,205(1):55-70. | 
| [6] | Dickinson M H, Lehman F O,Sane S P.Wing rotation and the aerodynamic basis of insect flight[J].Science,1999,284(5422):1954-1960. doi:  10.1126/science.284.5422.1954 | 
| [7] | Usherwood J R, Ellington C P. The aerodynamics of revolving wings—Ⅱ:Propeller force coefficients from mayfly to quail[J].J Exp Biol,2002,205(11):1565-1576. | 
| [8] | Ellington C P. The aerodynamics of hovering insect flight—Ⅲ:Kinematics[J].Philos Trans Roy Soc Lond,Ser B,1984,305(1122):41-78. doi:  10.1098/rstb.1984.0051 | 
| [9] | Ellington C P. The aerodynamics of hovering insect flight—Ⅳ:Aerodynamic mechanisms[J].Philos Trans Roy Soc Lond,Ser B,1984,305(1122):79-113. doi:  10.1098/rstb.1984.0052 | 
| [10] | Ellington C P. The aerodynamics of hovering insect flight—Ⅵ:Lift and power requirements[J].Philos Trans Roy Soc Lond,Ser B,1984,305(1122): 145-181. doi:  10.1098/rstb.1984.0054 | 
| [11] | Ennos A R. The kinematics and aerodynamics of the free flight of some Diptera[J].J Exp Biol,1989,142(1):49-85. | 
| [12] | Dudley R. The mechanics of forward flight in insects[D].Ph D thesis.Cambridge:Cambridge University, 1987. | 
| [13] | Wang H, Zeng L J, Yin C Y. Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing[J].Meas Sci Tech,2002,13(6): 903-908. doi:  10.1088/0957-0233/13/6/311 | 
| [14] | Ennos A R. The importance of torsion in the design of insect wings[J].J Exp Biol,1988,140(1):137-160. | 
| [15] | Ennos A R, Wootton R J. Functional wing morphology and aerodynamics of Panorpa germanica (insecta: Mecopter)[J].J Exp Biol,1989,143(1):267-284. | 
| [16] | Wootton R J, Herbert R C,Yong P G,et al.Approaches to the structural modeling of insect wings[J].Philos Trans Roy Soc Lond,Ser B,2003,358(1437):1577-1587. doi:  10.1098/rstb.2003.1351 | 
| [17] | Vogel S. Flight in Drosophila—Ⅲ:Aerodynamic characteristics of fly wings and wing models[J].J Exp Biol,1966,44(3):567-578. | 
| [18] | Dudley R, Ellington C P. Mechanics of forward flight in bumblebees—Ⅱ:Quasi-steady lift and power requirements[J].J Exp Biol,1990,148(1): 53-88. | 
| [19] | Thomas P D, Lombard C K. Geometric conservation law and its application to flow computations on moving grids[J].AIAA J,1979,17(10):1030-1037. doi:  10.2514/3.61273 | 
| [20] | Rogers S E, Kwak D. Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations[J].AIAA J,1990,28(2):253-262. doi:  10.2514/3.10382 | 
| [21] | Rogers S E, Kwak D, Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations[J].AIAA J,1991,29(4):603-610. doi:  10.2514/3.10627 | 
| [22] | Morton S A, Melville R B, Visbal M R. Accuracy and coupling issues of aeroelastic Navier-Stokes solutions on deforming meshes[J].J Aircraft,1998,35(5):798-805. doi:  10.2514/2.2372 | 
| [23] | Hilgenstock A. A fast method for the elliptic generation of three dimensional grid with full boundary control[A].In:Sengupta S, Hauser J, Eiseman P R,et al,Eds.Numerical Grid Generation in CFM’88[C].1988, Swansea UK: Pineridge Press Ltd,1988,137-146. | 
| [24] | Wu J H, Sun M. Unsteady aerodynamic forces of a flapping wing[J].J Exp Biol,2004,207(7):1137-1150. doi:  10.1242/jeb.00868 | 
| [25] | Fry S N, Sayaman R, Dickinson M H. The aerodynamics of hovering flight in Drosophila[J].J Exp Biol,2005,208(12):2303-2318. doi:  10.1242/jeb.01612 | 
| [26] | Wu J H, Sun M. Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight[J].Acta Mech Sinica,2005,21(3):207-217. doi:  10.1007/s10409-005-0039-5 | 
