Determination of the critical velocity of a straight wing with a high aspect ratio
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Department of Mathematics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, VIETNAM
Publication date: 2023-03-01
Corresponding author
Le Thi Thanh
International Journal of Applied Mechanics and Engineering 2023;28(1):105–117
An aerodynamic problem on an air flow around a large aspect ratio rectangular wing is investigated in this study. According to the theory of Vlasov, the wing is considered to be a thin rod. External loads are assumed to be proportional to the airfoil angle of attack related to the dimensionless coefficient of the lift and the pitching moment coefficient. These coefficients depend on the airfoil parameters and the Mach number M and are determined by experimental measurements for subsonic and supersonic velocities. In this case, to define the unstable cases of the wing, one bases on the Lyapunov stability theory. Equations of bending and torsional free vibrations have resulted. Based on the analysis of natural frequencies (eigenfrequencies), it is possible to determine the changing positions of the real part and the imaginary part of the characteristic equation solution. These positions can cause instabilities for the wing such as torsional divergence and flutter.
Fyn Ya.Ts. (1959): Introduction to the Theory of Aeroelasticity.– Moscow: Fizmatgiz, p.522.
Bisplinghoff R.L., Holt A. and Halfman R.L. (1996): Aeroelasticity.– Dover Publications, First Dover Edition, p.880.
Bisplinghoff R.L., Holt A. and Halfman R.L. (2013) Principles of Aeroelasticity.– Dover Publications; 2nd ed. edition, p.544.
Kohama Y. (1987): Some expectation on the mechanism of cross-flow instability in a swept wing flow.– Acta Mechanica, vol.66, pp.21-38, https://doi.org/10.1007/BF0118....
Ebrahimzade N., Dardel M. and Shafaghat R. (2016): Performance comparison of linear and nonlinear vibration absorbers in aeroelastic characteristics of a wing model.– Nonlinear Dyn, vol.86, pp.1075-1094, https://doi.org/10.1007/s11071....
Librescu L. and Marzocca P. (2005): Advances in the linear/nonlinear control of aeroelastic structural systems.– Acta Mechanica, vol.178, pp.147-186, https://doi.org/10.1007/s00707....
Jha S.K., Gautam U., Pawar P., Narayanan S. and Kumaraswamidhas L.A. (2020): Investigations of flow phenomena over a flat plate and NACA0012 airfoil at high angles of attack.– Iran J. Sci. Technol. Trans. Mech. Eng., vol.44, pp.985-996, https://doi.org/10.1007/s40997....
Manshadi M.D. and Jamalinasab M. (2017): Optimizing a two-element wing model with morphing flap by means of the response surface method.– Iran J. Sci. Technol. Trans. Mech. Eng., vol.41, pp.343-352 https://doi.org/10.1007/s40997....
Ying Zhen Li and Haukur Ingason (2017): Effect of cross section on critical velocity in longitudinally ventilated tunnel fires.– Fire Safety Journal, vol.91, pp.303-311, https://doi.org/10.1016/j.fire....
Mezher S.B., Connolly D.P., Woodward P.K, Laghrouche O., Pombo J. and Costa P.A. (2016): Railway critical velocity – Analytical prediction analysis.– Transportation Geotechnics, vol.6, pp.84-96, https://doi.org/10.1016/j.trge....
Stojanović V. and Petković M.D. (2018): Dynamic stability of vibrations and critical velocity of a complex bogie system moving on a flexibly supported infinity track.– Journal of Sound and Vibration, vol.434, p475-501, https://doi.org/10.1016/j.jsv.....
Tirronen M., Banichuk N., Jeronen J., Saksa T. and Tuovinen T. (2014): Stochastic analysis of the critical velocity of an axially moving cracked elastic plate.– Probabilistic Engineering Mechanics, vol.37, pp.16-23, https://doi.org/10.1016/j.prob....
Dimitrovová Z. and Varandas J.N. (2009): Critical velocity of a load moving on a beam with a sudden change of foundation stiffness: Applications to high-speed trains.– Computers & Structures, vol.87, Issues 19-20, p.1224-1232, https://doi.org/10.1016/j.comp....
Fazelzadeh S.A., Marzocca P., Mazidi A. and Rashidi E. (2010): Divergence and flutter of shear deformable aircraft swept wings subjected to roll angular velocity.– Acta Mech., vol.212, pp.151–165, https://doi.org/10.1007/s00707....
Volmir A.S. (1967): Stability of Deformable Systems.– Moscow, Nauka, p.984.
Algazin S.D. and Kiiko I.A. (2006): Flutter of Plates and Shells.– Moscow, Nauka, p.248.
Bolotin V.V. (1961): Non-conservative Problems in the Theory of Elastic Stability.– Moscow, Fizmatgiz, p.338.
Duan J. and Zhang Z. (2018): An efficient method for nonlinear flutter of the flexible wing with a high aspect ratio.– Aerospace Systems, vol.1, pp.49-62, https://doi.org/10.1007/s42401....
Lebedev A.A. and Chernobrovkin L.S. (1973): The Dynamics of the Flight of Unmanned Aerial Vehicles.– Moscow, Mashinostroenie, p.616.
Vlasov V.Z. (1959): Thin-Walled Elastic Rods.– Fizmatgiz, USSR, Moscow, p.574.
Das T. and Sircar R. (1986): Vibration of rectilinear plates on Vlasov's foundation at large amplitude.– Acta Mechanica, vol.61, pp.217-225, https://doi.org/10.1007/BF0117....
Alambeigi K., Mohammadimehr M., Bamdad M. and Rabczuk T. (2020): Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation.– Acta Mech., vol.231, pp.3199-3218, https://doi.org/10.1007/s00707....
Gurtin M.E. (1973): The Linear Theory of Elasticity.– In: Truesdell C. (eds) Linear Theories of Elasticity and Thermoelasticity, Springer, Berlin, Heidelberg, p.295.
Hetnarski R.B. and Ignaczak J. (2010): The Mathematical Theory of Elasticity.– CRC Press, p.837.
Gryazev M.V. (2011): Applied Problems of Solid Mechanics. Part 1. Statics of Rods.– Tula, Publishing House of TulSU, p.112.