Time-periodic stability of a flapping insect wing structure in hover

Journal of Aircraft

Volumn 46, Issue 2, 2009, Pages 450-464

  Rosenfeld, Nicholas C ^a,b   Wereley, Norman M ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b Department of Aerospace Engineering ^*

Author keywords

[No Author keywords available]

Indexed keywords

MICRO AIR VEHICLE (MAV); STABILITY; STIFFNESS; STRUCTURAL DESIGN; TIME DOMAIN ANALYSIS; WINGS;

FLAPPING FREQUENCY; FLAPPING WING MICRO AIR VEHICLE; FLOQUET ANALYSIS; NON-DIMENSIONAL EQUATIONS; OUT-OF-PLANE BENDING; PARAMETRIC INSTABILITIES; PARAMETRIC STABILITY; SCALABLE STABILITY;

EQUATIONS OF MOTION;

EID: 63349105929     PISSN: 00218669     EISSN: 15333868     Source Type: Journal    
DOI: 10.2514/1.34938     Document Type: Article

References (53)

1. Mueller, T. J., and DeLaurier, J. D., "An Overview of Micro Air Vehicle Aerodynamics," Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by T. Mueller, AIAA, New York, 2002, Chap. 1, pp. 1-10.
2. Bohorquez, F., Samuel, P., Sirohi, J., Pines, D., Rudd, L., and Perel, R., "Design, Analysis and Hover Performance of a Rotary Wing Micro Air Vehicle," Journal of the American Helicopter Society, Vol. 48, No. 2, April. 2003, pp. 80-90.
3. Grasmeyer, J. M., and Keennon, M. J., "Development of the Black Widow Micro Air Vehicle," Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, edited by T. Mueller, AIAA, New York, 2002 Chap. 24, pp. 519-535.
4. Ifju, P. G., "Flexible-Wing-Based Micro Air Vehicles," Compliant Structures in Nature and Engineering, edited by C. H. M. Jenkins, WIT Press, Billerica, MA, Chap. 8, 2005, pp. 171-191.
5. Lipera, L., Colbourne, J. D., Tischler, M. B., Mansur, M. H., Rotkowitz, M. C. and Patangui, P., "The Micro Craft iSTAR Micro Air Vehicle: Control System Design and Testing," Proceedings of the AHS 57th Annual Forum, American Helicopter Society, Washington, DC, pp. 1998-2008.
6. Ellington, C. P., "The Aerodynamics of Hovering Insect Flight: I. The Quasi-Steady Analysis," Philosophical Transactions of the Royal Society of London B, Biological Sciences, Vol. 305, No. 1122, Feb. 1984, pp. 1-15. doi:10.1098/rstb.1984.0049
7. Ellington, C. P., "The Aerodynamics of Hovering Insect Flight: III. Kinematics," Philosophical Transactions of the Royal Society of London B, Biological Sciences, Vol. 305, No. 1122, Feb. 1984, pp. 41-78. doi:10.1098/rstb.1984.0051
8. Dudley, R., The Biomechanics of Insect Flight: Form, Function, Evolution, Princeton Univ. Press, Princeton, NJ, 2002.
9. Videler, J. J., Avian Flight, Oxford Univ. Press, New York, NY, 2005.
10. Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A. R., Kram, R., and Lehman, S., "How Animals Move: An Integrative View," Science, Vol. 288, No. 5463, April 2000, pp. 100-106.
11. Sane, S. P., "The Aerodynamics of Insect Flight," Journal of Experimental Biology, Vol. 206, No. 23, Dec. 2003, pp. 4191-4208. doi:10.1242/jeb.00663
12. Wang, Z. J., "Dissecting Insect Flight," Annual Review of Fluid Mechanics, Vol. 37, 2005, pp. 183-210. doi:10.1146/annurev.fluid.36. 050802.121940
13. Ellington, C. P., "The Novel Aerodynamics of Insect Flight: Applications to Micro-Air Vehicles," Journal of Experimental Biology, Vol. 202, No. 23, Dec. 1999, pp. 3439-3448.
14. Żbikowski, R., "On. Aerodynamic Modelling of an Insect-Like Flapping Wing in Hover for Micro Air Vehicles," Philosophical Transactions of the Royal Society of London A, Vol. 360, No. 1791, Feb. 2002, pp. 273-290.
15. Ansari, S. A., Żbikowski, R., and Knowles, K., "Non-Linear Unsteady Aerodynamic Model for Insect- Like Flapping Wings in the Hover. Part 1: Methodology and Analysis," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 220, No. 2, April. 2006, pp. 61-83. doi:10.1243/09544100JAERO49
16. Ansari, S. A., Żbikowski, R., and Knowles, K., "Non-Linear Unsteady Aerodynamic Model for Insect- Like Flapping Wings in the Hover. Part 2: Implementation and Validation," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 220, No. 3, June 2006, pp. 169-186. doi:10.1243/09544100JAERO49
17. Singh, B., and Chopra, I., "Insect-Based Hover-Capable Flapping Wings for Micro Air Vehicles: Experiments and Analysis," AIAA Journal, Vol. 46, No. 9, Sept. 2008, pp. 2115-2135.
18. Ennos, A. R., "The Importance of Torsion in the Design of Insect Wings," Journal ofExperimental Biology, Vol. 40, No. 1, Nov. 1988, pp. 137-160.
19. Combes, S. A., and Daniel, T. L., "Into Thin Air: Contributions of Aerodynamic and Inertial-Elastic Forces to Wing Bending in the Hawkmoth Manduca Sexta," Journal of Experimental Biology, Vol. 206, No. 17, Sept. 2003, pp. 2999-3006. doi:10.1242/jeb.00502
20. Ellington, C. P., "The Aerodynamics of Hovering Insect Flight: VI. Lift and Power Requirements," Philosophical Transactions of the Royal Society of London B, Biological Sciences, Vol. 305, No. 1122, Feb. 1984, pp. 145-181. doi:10.1098/rstb.1984.0054
21. Ennos, A. R., "Inertial and Aerodynamic Torques on the Wings of Ditera in Flight," Journal of Experimental Biology, Vol. 142, No. 1, March 1989, pp. 87-95.
22. Combes, S.A., and Daniel, T. L., "Flexural Stiffness in Insect Wings: I. Scaling and the Influence of Wing Venation," Journal of Experimental Biology, Vol. 206, No. 17, Sept. 2003, pp. 2979-2987. doi:10.1242/jeb.00523
23. Norberg, R. Å, "The Pterostigma of Insect Wings an Inertial Regulator of Pitch," Journal of Comparative Physiology, Vol. 81, No. 1, 1972, pp. 9-22. doi:10.1007/BF00693547
24. Sunada, S., Zeng, L., and Kawachi, K., "The Relationship Between Dragonfly Wing Structure and Torsional Deformation," Journal of Theoretical Biology, Vol. 193, No. 1, July 1998, pp. 39-45. doi:10.1006/jtbl.1998.0678
25. Wootton, R. J., Herbert, R. C., Young, P. G., and Evans, K. E., "Approaches to the Structural Modelling of Insect Wings," Philosophical Transactions of the Royal Society of London B, Biological Sciences, Vol. 358, No. 1437, Sept. 2003, pp. 1577-1587. doi:10.1098/rstb.2003.1351
26. Combes, S. A., and Daniel, T. L., "Flexural Stiffness in Insect Wings: II. Spatial Distribution and Dynamic Wing Bending," Journal of Experimental Biology, Vol. 206, No. 17, Sept. 2003, pp. 2989-2997. doi:10.1242/jeb.00524
27. Herbert, R., Young, P. G., Smith, C. W., Wootton, R. J., and Evans, K. E., "The Hind Wing of the Desert Locust (Schistocerca Gregaria Forskål): III. A Finite Element Analysis of a Déployable Structure," Journal of Experimental Biology, Vol. 203, No. 19, Oct. 2000, pp. 2945-2955.
28. Kesel, A. B., Philippi, U., and Nachtigall, W., "Biomechanical Aspects of the Insect Wing: An Analysis Using the Finite Element Method," Computers in Biology and Medicine, Vol. 28, No. 4, July 1998, pp. 423-437. doi:10.1016/S0010-4825(98)00018-3
29. Smith, M. J. C., "Simulating Moth Wing Aerodynamics: Towards the Development of Flapping-Wing Technology," AIAA Journal, Vol. 34, No. 7, JuIy 1996, pp. 1348-1355. doi:10.2514/3.13239
30. Dickinson, M. H., Lehmann, F.-O., and Sane, S. P., "Wing Rotation and the Aerodynamic Basis of Insect Flight," Science, Vol. 284, No. 5422, June 1999, pp. 1954-1960. doi:10.1126/science.284.5422.1954
31. Mcintosh, S. H., Agawal, S. K., and Khan, Z., "Design of a Mechanism for Biaxial Rotation of a Wing for a Hovering Vehicle," IEEE/ASME Transactions on Mechatronics, Vol. 11, No. 2, April 2006, pp. 145-153. doi:10.1109/TMECH.2006.871089
32. Raney, D. L., and Slominski, E. C., "Mechanization and Control Concepts for Biologically Inspired Micro Air Vehicles," Journal of Aircraft, Vol. 41, No. 6, Nov.-Dec. 2004, pp. 1257-1265. doi:10.2514/1.5511
33. Singh, B., Ramasamy, M., Chopra, I., and Leishman, J. G., "Experimental Studies on Insect- Based Flapping Wings for Micro Hovering Air Vehicles," 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper 2005-2293, April. 2005.
34. Sitti, M., "Piezoelectrically Actuated Four-Bar Mechanism, with Two Flexible Links for Micromechanical Flying Insect Thorax," IEEE/ASME Transactions on Mechatronics, Vol. 8, No. 1, March 2003, pp. 26-36. doi:10.1109/TMECH.2003.809126
35. Yan,J., Avadhanula, S. A.,Birch, J., Dickinson,M. H., Sitti, M., Su, T., and Fearing, R. S., "Wing Transmission for a Micromechanical Flying Insect," Journal of Micromechatronics, Vol. 1, No. 3, 2001, pp. 221-237. doi:10.1163/156856301760132123
36. Żbikowski, R., Galiński, C., and Pedersen, C. B., "Four-Bar Linkage Mechanism for Insectlike Flapping Wings in Hover: Concept and an Outline of Its Realization," Journal of Mechanical Design, Vol. 127, No. 4, July 2005, pp. 817-824. doi:10.1115/1.1829091
37. Bilyk, D. J., "The Development of Flapping Wings for a Hovering Micro Air Vehicle," Master's Thesis, Univ. of Toronto, Toronto, 2000.
38. Wood, R. J., "The First Takeoff of a Biologically Inspired At-Scale Robotic Insect," IEEE Transactions on Robotics and Automation, Vol. 24, No. 2, April 2008, pp. 341-347.
39. Richards, J. A., Analysis of Periodically Time-Varying Systems, Springer-Verlag, New York, NY, 1983.
40. Willmott, A. P., and Ellington, C. P., "The Mechanics of Flight in the Hawkmoth Manduca Sexta: II. Aerodynamic Consequences of Kinematic and Morphological Variation," Journal of Experimental Biology, Vol. 200, No. 21, Nov 1997, pp. 2723-2745.
41. Leishman, J. G., Principles of Helicopter Aerodynamics, Cambridge Univ. Press, New York, NY, 2nd ed., 2006.
42. Combes, S. A., Wing Flexibility and Design for Animal Flight, Ph.D. Dissertation, Univ. of Washington, July 2002.
43. Houbolt, J. C., and Brooks, G. W., "Differential Equations of Motion for Combined Flapwise Bending, Chordwise Bending, and Torsion of Twisted Nonuniform Rotor Blades," NACA Report No. 1346, 1958.
44. Kunz, D. L., "Survey and Comparison of Engineering Beam Theories for Helicopter Rotor Blades," Journal of Aircraft, Vol. 31, No. 3, May-June 1994, pp. 473-479. doi:10.2514/3.46518
45. Hodges, D. H., and Dowell, E. H., "Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades," NASA Technical Note TN-D-7818, 1974.
46. Rosenfeld, N. C., "Time-Periodic Stability of Flapping Insect and Micro Air Vehicle Wing Structures," Ph.D. Dissertation, Univ. of Maryland, College Park, MD (in preparation).
47. Meirovitch, L., Fundamentals of Vibrations, McGraw-Hill, New York, NY, 2001.
48. Weis-Fogh, T., "Quick Estimates of Flight Fitness in Hovering Animals, Including Novel Mechanisms for Lift Production," Journal of Experimental Biology, Vol. 59, No. 1, Aug. 1973, pp. 169-230.
49. Willmott, A. P., and Ellington, C. P., "The Mechanics of Flight in the Hawkmoth Manduca Sexta: I. Kinematics of Hovering and Forward Flight," Journal of'Experimental Biology, Vol.200, No. 21, Nov. 1997, pp. 2705-2722.
50. Chai, P., and Millard, D., "Flight and Size Constraints: Hovering Performance of Large Hummingbirds Under Maximal Loading," Journal of Experimental Biology, Vol. 200, No. 21, Nov. 1997, pp. 2757-2763.
51. Sane, S. P., and Dickinson, M. H., "The Control of Flight Force by a Flapping Wing: Lift and Drag Production," Journal of Experimental Biology, Vol. 204, No. 15, Aug. 2001, pp. 2607-2626.
52. Dormand, J. P., and Prince, P. J., "A Family of Embedded Runge-Kutta Formulae," Journal of Computational and Applied Mathematics, Vol. 6, No. 1, March 1980, pp. 19-26. doi:10.1016/0771-050X(80)90013-3
53. Johnson, W., Helicopter Theory, Dover, Mineola, NY, 1994.