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Flutter Analysis of a Tapered Viscoelastic Wing Subjected to a Follower Thrust Force

Youssef S. Matter(1), Tariq Taha Darabseh(2*), Abdel-Hamid I. Mourad(3)

(1) United Arab Emirates University, United Arab Emirates
(2) United Arab Emirates University Mechanical Engineering Department, United Arab Emirates
(3) United Arab Emirates University, United Arab Emirates
(*) Corresponding author



The flutter instability of a wing considering many parameters is investigated. The effects of the structural damping, wing taper ratio, engine thrust, and engine mass and location on the flutter characteristics of the wing are studied. The material of the wing is modeled as a viscoelastic material where Kelvin-Voigt model is used to represent the viscoelastic behavior of the material. The unsteady Theodorsen theory is used to model the aerodynamic forces (i.e. lift and pitching moment). The governing equations of motion are developed using the extended Hamilton’s principle and solved via Galerkin’s method along with the classical flutter investigation approach. The developed model is validated against the well-known Goland wing and HALE wing. The flutter determinant method is employed to carry out non-dimensional parametric study on the Goland wing. The study revealed that a tapered wing would be more dynamically stable than a uniform wing. It is also observed that the viscoelastic damping provides wider stability region for the wing. This work shows that the engine thrust and mass have significant effects on the dynamic stability of the wing.
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Aeroelasticity; Viscoelastic Material; Flutter; Kelvin-Voigt Model; Galerkin’s Method; Theodorsen; Follower Force

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M. Goland, The flutter of a uniform cantilever wing, Journal of Applied Mechanics-Transactions of the Asme 12.4 (1945), A197-A208.

M. Goland and Y. L. Luke, The flutter of a uniform wing with tip weights, Journal of Applied Mechanics 15.1 (1948), 13-20.

Y. C. Fung, An introduction to the theory of aeroelasticity. (Courier Dover Publications, 2008).

L. Meirovitch, Elements of vibration analysis. (McGraw-Hill Companies, 1975).

M. R. Moosavi, A. N. Oskouei and A. Khelil, Flutter of subsonic wing, Thin-walled structures 43.4 (2005), 617-627.

A. H. Nayfeh, M. Ghommem and M. R. Hajj, Normal form representation of the aeroelastic response of the Goland wing, Nonlinear Dynamics 67.3 (2012), 1847-1861.

M. Ghommem, M. R. Hajj and A. H. Nayfeh, Uncertainty analysis near bifurcation of an aeroelastic system, Journal of Sound and Vibration 329.16 (2010), 3335-3347.

A. Abdelkefi, A. H. Nayfeh and M. R. Hajj, Design of piezoaeroelastic energy harvesters, Nonlinear Dynamics 68.4 (2012), 519-530.

A. Abdelkefi, et al, An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system, Nonlinear Dynamics 71.1-2 (2013), 159-173.

H. Haddadpour and R. D. Firouz-Abadi, Evaluation of quasi-steady aerodynamic modeling for flutter prediction of aircraft wings in incompressible flow, Thin-walled structures 44.9 (2006), 931-936.

T. T. Darabseh and J. Genin, Dynamic Stability of Viscoelastic Columns Loaded by a Follower Force, Journal of Mechanical Engineering Science, 218.10 (2004), 1091-1101.

H. H. Hilton and C. Vail, Bending-torsion flutter of linear viscoelastic wings including structural damping, 34th Structures, Structural Dynamics and Materials Conference (1993).

P. C. Martins, D. A. Rade and F. D. Marques, Dynamic stability analysis of aeroviscoelastic systems, The 22nd international congress of mechanical engineering (COBEM 2013), November Ribeirão Preto, SP, Brazil.

S. Yi, M. F. Ahmad and H. H. Hilton, Dynamic responses of plates with viscoelastic free layer damping treatment, Journal of vibration and acoustics 118.3 (1996), 362-367.

W. T. Feldt, and G. Herrmann, Bending-torsional flutter of a cantilevered wing containing a tip mass and subjected to a transverse follower force, Journal of the Franklin Institute 297.6 (1974), 467-478.

D. H. Hodges, M. J. Patil and S. Chae, Effect of thrust on bending-torsion flutter of wings, Journal of Aircraft 39.2 (2002), 371-376.

S. A. Fazelzadeh, A. Mazidi and H. Kalantari, Bending-torsional flutter of wings with an attached mass subjected to a follower force, Journal of Sound and Vibration 323.1-2 (2009), 148-162.

R. D. Firouz-Abadi, A. R. Askarian and P. Zarifian, Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow, Journal of Fluids and Structures 36 (2013), 18-31.

M. R. Amoozgar, S. Irani and G. A. Vio, Aeroelastic instability of a composite wing with a powered-engine, Journal of Fluids and Structures 36 (2013), 70-82.

A. Mazidi, H. Kalantari and S. A. Fazelzadeh, Aeroelastic response of an aircraft wing with mounted engine subjected to time-dependent thrust, Journal of Fluids and Structures 39 (2013), 292-305.

T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter, NACA Thecnical Report 496 (1935).

D. H. Hodges, and G. A. Pierce, Introduction to structural dynamics and aeroelasticity. Vol. 15. (Cambridge university press, 2011).

M. J. Patil, D. H. Hodges and C. E. S. Cesnik, Nonlinear aeroelasticity and flight dynamics of high-altitude long-endurance aircraft, Journal of Aircraft 38.1 (2001), 88-94.

M. Mahran, H. Negm and A. El-Sabbagh, Aero-elastic characteristics of tapered plate wings, Finite Elements in Analysis and Design 94 (2015), 24-32.

S. Durmaz, O. O. Ozgumus and M. O. Kaya, Aeroelastic Analysis of a Tapered Aircraft Wing, Ankara International Aerospace Conference, METU, Ankara (2007).

F. Beheshtinia, R. D. Firouz-Abadi, and M. Rahmanian, Viscous damping effect on the aeroelastic stability of subsonic wings: Introduction of the U–K method, Journal of Fluids and Structures 73 (2017), 1-15.

Boulhafa, E., Kouddane, R., Ouadfel, H., Self-Consistent Approach in Elasto-viscoplasticity of Heterogeneous Materials, (2018) International Review of Mechanical Engineering (IREME), 12 (10), pp. 847-853.


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