Abstract
This paper presents an efficient modelling of autonomous flexible airships. These flying objects lighter than air (L.T.A.) are assumed to undergo large rigid-body motion and small elastic deformation. The formalism used is based on the Euler–Lagrange approach. The airship considered in this study is represented by a flexible ellipsoid of revolution. The coupling between the added masses issued from the overall body motion and those issued from the elasticity was determined by means of the velocity potential flow theory. We develop a fully analytical methodology with some assumptions. This feature distinguishes the current work from earlier treatments of the coupling, it allows one to minimise the number of degrees of freedom of the dynamical model, and renders the model suitable for use in the algorithms of stabilisation and trajectory generation. Numerical simulations are presented at the end of this paper. They underline the interest of the developed theoretical results.
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Khoury, G.A., Gillet, J.D.: Airship Technology. Cambridge University Press, Cambridge (1999)
Azouz, N., Bestaoui, Y., Lemaitre, O.: Dynamic analysis of airships with small deformations. In: Proceedings of 3rd IEEE Workshop on Robot Motion and Control, Poland (2002)
Li, Y., Nahon, M., Sharf, I.: Dynamics modeling and simulation of Flexible Airships. AIAA J. 47(3), 592–601 (2009)
Liao, L., Pasternak, I.: A review of airship structural research and developments. Prog. Aerosp. Eng. 45(4–5), 83–96 (2009)
Bestaoui, Y., Hamel, T.: Dynamic modeling of small autonomous blimps. In: Proceedings of IEEE Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, pp. 579–584 (2000)
Pettit, C.L.: Uncertainty quantification in aeroelasticity: recent results and research challenges. J. Aircr. 41(5), 1217–1229 (2004)
Bianchin, M., Quaranta, G., Mantegazza, P.: State space reduced order models for static aeroelasticity and flight mechanics of flexible aircrafts. In: 17th National Conference AIDAA, Italy (2003)
Simo, J.C.: The role of non-linear theories in transient dynamic analysis of flexible aircrafts. J. Sound Vib. 119, 487–508 (1987)
Roskam, J.: Flight Performance of Fixed and Rotary Wing Aircraft. Butterworth/Heinemann, Stoneham/London (2006)
Tuzcu, I.: On the stability of flexible aircraft. Aerosp. Sci. Technol. 12(5), 376–384 (2008)
Pounds, P., Mahony, R., Hynes, P., Roberts, J.: Design of a four-rotor aerial robot. In: Transactions of Australian Conference on Robotics and Automation, pp. 145–150 (2002)
Boyer, F., Coiffet, Ph.: Generalization of Newton-Euler model for flexible manipulators. J. Robot. Syst. 13(1), 11–24 (1998)
Bennaceur, S., Azouz, N., Abichou, A.: Modeling and control of flexible blimps. In: Transactions of AIP Mediterranean Conference CISA’08, Annaba, vol. 1019, pp. 397–407 (2008)
Bathe, K.J., Ramm, E., Wilson, E.L.: Finite elements for large deformation dynamic analysis. Int. J. Numer. Methods Eng. 9, 353–386 (1975)
Bennaceur, S., Azouz, N., Boukraa, D.: An efficient modelling of flexible Airships: Lagrangian approach. In: Proceeding of the ESDA’06 ASME International Conference, Torino, Italy (2006)
Yang, J., Lei, F., Xie, X.: Dynamic Analysis of Fluid-Structure Interaction on Cantilever Structure. Springer, Netherlands (2009)
De Langre, E., Païdoussis, M., Doaré, O., Modarres-Sadeghi, Y.: Flutter of long flexible cylinders in axial flow. J. Fluid Mech. 571, 371–389 (2007)
Fossen, T.: Guidance and Control of Ocean Vehicles. Wiley, Chichester (1996)
El Omari, K., Schall, E., Koobus, B., Dervieux, A., Amara, M., Dumas, J.-P.: Fluid-structure coupling of a turbulent flow and a generic blimp structure. In: Transactions of the Mathematical Symposium Garcia de Galdeano, Spain, vol. 33, pp. 369–376 (2006)
Taylor, R.L., Makerle, J.: Fluid-structure interaction approach and boundary elements approach. Finite Elem. Anal. Des. 31, 231–240 (2006)
Liu, J., Lu, C., Xue, L.: Investigation of airship aeroelasticity using fluid-structure interaction. J. Hydrodyn. Ser. B 20(2), 164–171 (2008)
Bessert, N., Frederich, O.: Nonlinear airship aeroelasticity. J. Fluids Struct. 21, 731–742 (2005)
Gibert, R.-J.: Vibrations des structures. Interactions avec les fluides. Eyrolles, Paris (1988)
Shabana, A.: Dynamics of Multibody Systems. Springer, Berlin (2005)
Zienckiewicz, O.C., Taylor, R.L.: The Finite Element Method, 4th edn. McGraw-Hill, New York (1997)
Hygounenc, E., Kyun Jung, II, Soueres, Ph., Lacroix, S.: The autonomous blimp project of LAAS-CNRS: achievements in flight control and terrain mapping. Int. J. Robot. Res. 23(4–5), 473–511 (2004)
Lamb, H.: On the Motion of Solids Through a Liquid. Hydrodynamics, 6th edn. Dover, New York (1945)
Macagno, E.O., Landweber, L.: Irrotational motion of the liquid surrounding a vibrating ellipsoid of revolution. J. Ship Res. 2(1), 37–49 (1958)
Lewis, F.M.: The inertia of the water surrounding a vibrating ship. In: Transactions of the 37th General Meeting of the SNAME, New York, vol. 37, pp. 1–20 (1929)
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Bennaceur, S., Azouz, N. Contribution of the added masses in the dynamic modelling of flexible airships. Nonlinear Dyn 67, 215–226 (2012). https://doi.org/10.1007/s11071-011-9973-x
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DOI: https://doi.org/10.1007/s11071-011-9973-x