Determination of the Flutter Instability Boundary of a Composite Wing Using Support Vector Machine

Document Type : Research Article

Authors

Faculty of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

The main goal of this article is to train a support vector machine in order to determine the boundary of the composite wing aeroelastic instability. Aircraft wing is modeled as a cantilever beam with two degrees of freedom with thrust as a follower force and mass of the engine. For structural modeling of composite wing the layer theory has been used and in the aerodynamic model, the flow has been assumed to be unsteady, subsonic and incompressible. Using the assumed mode method, the wing dynamic equations of the motion have been derived by Lagrange equations. Linear flutter speed according to the eigenvalues of the motion equations has been calculated. The process of flutter speed calculation has been converted to a computer code in which the number of layers, angle of fibers in each layer, the mass of the engine, and the thrust are input variables and the flutter speed is its output. Determination of the instability boundary using this conventional method is time consuming. In this article, a support vector machine has been adopted to reduce the calculation cost. The results indicate that support vector machine can be used in determining the boundary of the wings flutter instability as an accurate and fast tool.

Keywords

Main Subjects


[1]  A. Basudhar, S. Missoum, Adaptive explicit decision functions for probabilistic design and optimization using support vector machines, Computers & Structures, 86(19-20) (2008) 1904-1917.
[2]  F. Khan, F. Enzmann, M. Kersten, Multi-phase classification by a least-squares support vector machine approach in tomography images of geological samples, Solid Earth, 7(2) (2016) 481-492.
[3]  S. Tong, D. Koller, Support vector machine active learning with applications to text classification, Journal of machine learning research, 2(Nov) (2001) 45-66.
[4]  R.L. Bisplinghoff, H. Ashley, Principles of aeroelasticity, Courier Corporation, 2013.
[5]  Y.C. Fung, An introduction to the theory of aeroelasticity, Courier Dover Publications, 2008.
[6]  W.T. Feldt, 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.
[7]  D.H. Hodges, M.J. Patil, S. Chae, Effect of thrust on bending-torsion flutter of wings, Journal of Aircraft, .673-173 (2002) (2)93
[8]  A. Mazidi, S. Fazelzadeh, Flutter of a swept aircraft wing with a powered engine, Journal of Aerospace Engineering, 23(4) (2009) 243-250.
[9]  M. Amoozgar, S. Irani, G. Vio, Aeroelastic instability of a composite wing with a powered-engine, Journal of Fluids and Structures, 36 (2013) 70-82.
[10]  R. Koohi, H. Shahverdi, H. Haddadpour, Nonlinear aeroelastic analysis of a composite wing by finite element method, Composite Structures, 113 (2014) 118-126.
[11]  M.R. Fallah, M. Farrokh, S. Irani, The effect of laminate layers and follower force on optimum flutter speed of composite wing, Modares Mechanical Engineering, 16(6) (2016) 226-236.(in Persian)
[12]  V. Vapnik, Statistical learning theory, Wiley, New York, 1998.
[13]  V. Vapnik, The nature of statistical learning theory, Springer science & business media, 2013.
[14]  Q. Pan, D. Dias, An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation, Structural Safety, 67 (2017) 85-95.
[15]  E. Dowell, E. Crawley, H. Curtiss Jr, D. Peters, R. Scanlan, F. Sisto, A Modern Course in Aeroelasticity, in, Kluwer Academic Publishers, Dodrecht, 1995.
[16]  C. Cesnik, D. Hodges, M. Patil, Aeroelastic analysis of composite wings, in:  37th Structure, Structural Dynamics and Materials Conference, 1996, pp. 1444.
[17]  H. Pourshamsi, A. Mazidi, S.A. Fazelzadeh, Flutter analysis of an aircraft wing carrying, elastically, an external store, Modares Mechanical Engineering, 15(1) (2015).(in Persian).
[18]  S. Fazelzadeh, A. Mazidi, H. Kalantari, Bendingtorsional flutter of wings with an attached mass subjected to a follower force, Journal of Sound and Vibration, 323(1-2) (2009) 148-162.
[19]  D.H. Hodges, E. Dowell, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades,  (1974).
[20]  A.A.A.-H. Ali, M.I. Hamed, The effect of laminated layers on the flutter speed of composite wing, Journal of Engineering, 18(8) (2012) 924-934.
[21]  B. Ghadiri, M. Razi, S. Hamidi, Dynamic instability analysis of a swept wing in time-domain, Modares Mechanical Engineering, 9(37) (2011) 93-106.(in Persian)
[22] M.J. Patil, D.H. Hodges, C.E. Cesnik, Limit-cycle oscillations in high-aspect-ratio wings, Journal of fluids and structures, 15(1) (2001) 107-132.
[23] E.L. Brown, Integrated strain actuation in aircraft with highly flexible composite wings, Massachusetts Institute of Technology, 2003.