Abstract
This chapter deals with the dynamics of elastic structures: unswept fixed-wing and free-free wings, modeled as beams of zero thickness, linear as well as nonlinear. The main concern is with spectral analysis, modes and mode shapes as a means to study stability. The language is that of abstract functional analysis: Hilbert spaces and semigroup theory of operators for time domain description.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mikhlin, S.G.: Mathematical Physics, an Advanced Course. North-Holland, Amsterdam (1970)
Thompson, P.A.: Compressible Fluid Dynamics. McGraw-Hill, New York (1972)
Van Dyke, M.: Perturbation Methods in Fluid Mechanics. The Parabolic Press, California (1975)
Hodges, D.H., Pierce, G.A.: Introduction to Structural Dynamics and Aeroelasticity. Cambridge University Press, Cambridge (2007)
Bisplinghoff, R.L., Ashley, H., Halfman, R.L.: Aeroelasticity. Addison-Wesley, Cambridge (1955)
Hille, E., Phillips, R.S.: Functional Analysis and Semigroups. American Mathematical Society, Providence (1957)
Tricomi, F.G.: Integral Equations. Dover Publications, New York (1955)
Balakrishnan, A.V.: Applied Functional Analysis. Springer, New York (1980)
Kuethe, A.M., C-Y. Chow: Foundations of Aerodynamics. John Wiley, New York (1976)
Butzer, P.L., Nessel, R.J.: Fourier Analysis and Approximation, vol. 1. Academic Press, New York (1971)
Carracedo, C.M., Alix, M.S.: The Theory of Fractional Powers of Operators. Elsevier, Amsterdam (2001)
Timoshenko, S.: Vibration Problems in Engineering, 2nd edn. Van Nostrand, New York (1937)
Timoshenko, S., Young, D.H.: Vibration Problems in Engineering. Van Nostrand Reinhold, Dordrecht (1955)
Landhal, M.T.: Unsteady Transonic Flow. Pergammon, New York (1961)
Rudin, W.: Real Complex Analysis. McGraw–Hill, New York (1966)
Balakrishnan, A.V.: Dynamics and Control of Articulated Anisotropic Timoshenko beams In: Tzou, H.S., Bergman, L.A. (ed.) Dynamics and Control of Distributed Systems. Cambridge University Press, Cambridge (1998)
Balakrishnan, A.V.: On the nonnumeric mathematical foundations of linear aeroelasticity. In: Sivasundaram, S. (ed.) Proceedings ICNPAA, August 2002
Balakrishnan, A.V.: Possio Integral Equation of Aeroelasticity. J. Aero. Eng. 16(4), 138–154 October (2003)
Balakrishnan, A.V.: Control of flexible flight structures. In: Analyse Mathematique et Applications, Gauthier-Villars (1988)
Balakrishnan, A.V.: Theoretical Limits of Damping Attainable by Smart beams with rate feedback. In: Proceedings of the SPIE, vol. 3039 (1997)
Balakrishnan, A.V.: Damping operators in continuum models of flexible flight structures. Explicit models for proportional damping in Beam Torsion. J. Differ. Integr. Equat. 13 (1990)
Balakrishnan, A.V.: Control of structures with selfstraining actuators: coupled Euler/Timoshenko model: I. In: Sivasundaram, S. (ed.) NonLinear Problems in Aviation and Aerospace, Gordon and Breach, Amsterdam (2000)
Beran, P.S., Straganac, T.W., Kim, K.: Studies of store induced Limit Cycle Oscillations Using a model with full system nonlinearities. AIAA 1730, 2003–1730.
Dowell, E.H., Traybar, J., Hodges, H.: An experimental theoretical study of nonlinear bending and torsion deformations of a cantilever bar. J. Sound Vib. 533–544 (1977).
Goland, M., Luke, M.L.: The flutter of a uniform wing with tip weights. J. Appl. Math. 15(1) (1948).
Goland, M.: The flutter of a uniform cantilever wing. J. Appl. Mech. 12, 197–208 (1945)
Alvarez–Salazar, O.S., Iliff, K.W.: Destabilizing effects of rate feedback on strain actuated beams. J. Sound Vib. 221(2), 289–307 (1999)
Majda, A.: Disappearing solutions for the dissipative wave equation. Indiana J. Math. 24(12), 132–164 (1975)
Patil, M.J., Hodges, D.H.: Flight dynamics of highly flexible flying wings. AIAA J. Aircr. 43(6), 1790–1799 (2006)
Su, W., Cesnick, C.E.S.: Dynamic response of highly flexible flying wings. AIAA J. 49, 324–339 (2011)
Balakrishan, A.V.: Explicit LQG optimised control laws for flexible structures/collocated rate sensors. AIAA 94–1657. Adaptive Structures Forum, La Jolla (1993)
Tuffaha, A.: Flutter stability analysis of a wedge shaped airfoil with nonzero thickness in nonviscous air flow. NonLinear Stud. I S publishers 16(3), 235–257 (2009)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Balakrishnan, A.V. (2012). Dynamics of Wing Structures. In: Aeroelasticity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3609-6_2
Download citation
DOI: https://doi.org/10.1007/978-1-4614-3609-6_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3608-9
Online ISBN: 978-1-4614-3609-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)