[en] A closed form state-space model for the nonlinear aeroelastic response of thin cantilevered flat plates is derived using a combination of von Karman thin plate theory and a linearized continuous time vortex lattice aerodynamic model. The modal-based model is solved for the amplitude and period of the limit cycles of the flat plates using numerical continuation. The resulting predictions are compared to experimental data obtained from identical flat plates in the wind tunnel. Both conventional and topologically optimised flat rectangular plates are investigated. It is shown that the aeroelastic model predicts the linear flutter conditions and nonlinear response of the plates with reasonable accuracy, although the predicted limit cycle amplitude variation with airspeed is different to the one measured experimentally due to unmodelled physics.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Munk, D. J.; Defence Science and Technology > Aerospace Division
Dooner, D.; University of Sydney > School of Aerospace, Mechanical and Mechatronic Engineering
Best, F.; University of Sydney > School of Aerospace, Mechanical and Mechatronic Engineering
Vio, G. A.; University of Sydney > School of Aerospace, Mechanical and Mechatronic Engineering
Giannelis, N. F.; Sydney > School of Aerospace, Mechanical and Mechatronic Engineering
Murray, A. J.; University of Sydney > School of Aerospace, Mechanical and Mechatronic Engineering
Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale
Language :
English
Title :
Limit cycle oscillations of cantilever rectangular wings designed using topology optimisation
Publication date :
January 2020
Event name :
AIAA SciTech 2020 Forum and Exhibition
Event organizer :
American Institute of Aeronautics and Astronautics
G. Dimitriadis, N.F. Giannelis, and G.A. Vio. A modal frequency-domain generalised force matrix for the unsteady vortex lattice method. Journal of Fluids and Structures, 76:216–228, 2018.
Y. Weiliang and E. H. Dowell. Limit cycle oscillation of a fluttering cantilever plate. AIAA Journal, 29(11):1929– 1936, 1991.
D. Tang, M. Zhao, and E. H. Dowell. Inextensible beam and plate theory: Computational analysis and comparison with experiment. ASME Journal of Applied Mechanics, 81(6), 2014.
D. Tang, E. H. Dowell, and K. C. Hall. Limit cycle oscillations of a cantilevered wing in low subsonic flow. AIAA Journal, 37(3):364–371, 1999.
D. Tang, J. K. Henry, and E. H. Dowell. Limit cycle oscillations of delta wing models in low subsonic flow. AIAA Journal, 37(11):1355–1362, 1999.
P.J. Attar and R.E. Gordnier. Aeroelastic prediction of the limit cycle oscillations of a cropped delta wing. Journal of Fluids and Structures, 22(1):45–58, 2001.
P. J. Attar. Cantilevered plate Rayleigh-Ritz trial function selection for von Kármán’s plate equations. Journal of Aircraft, 44(2):654–661, 2007.
P.J. Attar, E.H. Dowell, and D.M. Tang. A theoretical and experimental investigation of the effects of a steady angle of attack on the nonlinear flutter of a delta wing plate model. Journal of Fluids and Structures, 17(2):243– 259, 2003.
D. Tang and E. H. Dowell. Effects of angle of attack on nonlinear flutter of a delta wing. AIAA Journal, 39(1):15–21, 2001.
B. Korbahti, E. Kagambage, T. Andrianne, N. Abdul Razak, and G. Dimitriadis. Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel. Journal of Fluids and Structures, 27(3):408–426, 2011.
D. J. Munk, G. A. Vio, and G. P. Steven. Topology and shape optimization methods using evolutionary algorithms: a review. Structural and Multidisciplinary Optimization, 52(3):613–631, 2015.
M. P. Bendsøe and N. Kikuchi. Generating optimal topologies in structural design using a homogenization method. Computer methods in applied mechanics and engineering, 71(2):197–224, 1988.
O.M. Querin, G.P. Steven, and Y.M. Xie. Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Engineering Computations, 15:1031–1048, 1998.
X. Huang and Y.M. Xie. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, 43:1039–1049, 2007.
X. Huang, Z.H. Zuo, and Y.M. Xie. Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Computers & structures, 88(5-6):357–364, 2010.
D.J. Munk, G.A. Vio, and G.P. Steven. A simple alternative formulation for structural optimisation with dynamic and buckling objectives. Structural and Multidisciplinary Optimization, 55(3):969–986, 2017.
G. Dimitriadis. Introduction to nonlinear aeroelasticity. John Wiley & Sons, Inc., Chichester, West Sussex, UK, 2017.
J. Katz and A. Plotkin. Low Speed Aerodynamics. Cambridge University Press, 2001.
R. J. S. Simpson, R. Palacios, and J. Murua. Induced-drag calculations in the unsteady vortex lattice method. AIAA Journal, 51(7):1775–1779, 2013.
K. L. Roger. Airplane math modelling methods for active control design. Report AGARD-CP-228, AGARD, 1977.
O. Sigmund and J. Petersson. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization, 16(1):68–75, 1998.
M. P. Bendsøe and O. Sigmund. Material interpolation schemes in topology optimization. Archive of applied mechanics, 69(9-10):635–654, 1999.
W. Prager. Optimality criteria in structural design. Proceedings of the National Academy of Sciences, 61(3):794– 796, 1968.
N. L. Pedersen. Maximization of eigenvalues using topology optimization. Structural and multidisciplinary optimization, 20(1):2–11, 2000.
D.J. Munk, G.A. Vio, and G.P. Steven. A bi-directional evolutionary structural optimisation algorithm with an added connectivity constraint. Finite Elements in Analysis and Design, 131:25–42, 2017.
A. P. Seyranian, E. Lund, and N. Olhoff. Multiple eigenvalues in structural optimization problems. Structural optimization, 8(4):207–227, 1994.
D.J. Munk, G.A. Vio, and G.P. Steven. Novel moving isosurface threshold technique for optimization of structures under dynamic loading. AIAA Journal, 55(2):638–651, 2017.
