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Limit-cycle oscillation prediction for non-linear aeroelastic systems

Published online by Cambridge University Press:  04 July 2016

A. Sedaghat
Affiliation:
The Manchester School of Engineering, The University of Manchester, Manchester, UK
J. E. Cooper
Affiliation:
The Manchester School of Engineering, The University of Manchester, Manchester, UK
J. R. Wright
Affiliation:
The Manchester School of Engineering, The University of Manchester, Manchester, UK
A. Y. T. Leung
Affiliation:
The Manchester School of Engineering, The University of Manchester, Manchester, UK

Abstract

This paper describes part of an investigation into the prediction and characterisation of limit cycle oscillations occurring in non-linear aeroelastic systems. Through the use of a modified version of normal form theory, it is shown how it is possible to predict the limit-cycle oscillations and characterise their stability. The approach is analytical and does away with the need for an excessive amount of time marching iterative numerical simulation of the system. The methodology is demonstrated upon a simple two degrees-of-freedom aeroelastic wing model with cubic stiffness. A good agreement was obtained between the analytical prediction and numerical simulations.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2002 

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References

1. AGARD CP 566, Advanced Aeroservoelastic Testing and Data Analysis, 1995.Google Scholar
2. Price, S.J., Alighanbari, H. and Lee, B.H.K. The aeroelastic response of a 2-dimensional aerofoil with bilinear and cubic structural non-linearities, J Fluid and Structures, 1995, 9, pp 175193.Google Scholar
3. Dimitriadis, G. and Cooper, J.E. Limit cycle oscillation control and suppression, Aeronaut J, 1999, 103, (1023), pp 257263.Google Scholar
4. Dreim, D.R., Jacobson, S.B. and Britt, R.T. Simulation of non-lnear transonic aeroelastic behaviour of the B–2, Int Forum on Aeroelasticity and Structural Dynamics, 1999, pp 511522.Google Scholar
5. Mastroddi, F. and Bettoli, A. Non-linear aeroelastic system identification via wavelet analysis in the neighbourhood of a limit cycle, Int Forum on Aeroelasticity and Structural Dynamics, 1999, pp 857866.Google Scholar
6. Denegri, C.M. and Johnson, M.R. Limit cycle oscillation prediction using artificial neural networks, Int Forum on Aeroelasticity and Structural Dynamics, 1999, pp 7180.Google Scholar
7. Liu, L., Wong, Y.S. and Lee, B.H.K. Application of the centre manifold theory in non-linear aeroelasticity, Int Forum on Aeroelasticity and Structural Dynamics, 1995, pp 533542.Google Scholar
8. Holden, M., Brazier, R. and Cal, A. Effects of structural non-linearities on a tailplane flutter mode, Int Forum on Aeroelasticity and Structural Dynamics, 1995, paper 60.Google Scholar
9. Ruiz-Calavera, L. et al. A new compendium of unsteady aerodynamic test cases for CFD, Int Forum on Aeroelasticity and Structural Dynamics, 1999, pp 112.Google Scholar
10. AGARD CP 507, Transonic Unsteady Aerodynamics and Aeroelasticity, 1992.Google Scholar
11. AGARD CP 822, Numerical Unsteady Aerodynamics and Aeroelastic Simulation, 1998.Google Scholar
12. Kryloff, N. and Bogoliuboff, N. Introduction to Non-Linear Mechanics, Princeton University Press, 1947.Google Scholar
13. Leung, A.Y.T., Zhang, Q.C. and Chen, Y.S. Normal form analysis of Hopf bifurcation exemplified by Duffing’s equation, J Shock and Vibration, 1994, 1, pp 233240.Google Scholar
14. Hancock, G.J., Wright, J.R. and Simpson, A. On the teaching of the principles of wing flexure-torsion flutter, Aeronaut J, 1985, 89, (888) pp 285305.Google Scholar
15. Dimitriadis, G. Implementation and Comparison of Three Methods of Modelling the Effect of the Aerodynamic Forces on the Aeroelastic Behaviour of a Simple Wing, MSc Thesis, The University of Manchester, Aerospace Engineering Department, 1995.Google Scholar
16. Fung, Y.C. An Introduction to the Theory of Aeroelasticity, Wiley, New York, 1995.Google Scholar
17. Poincare, H. Les Methods Nouvelles de la Mecanique Celeste, Gauthier-Villars, Paris, 1889.Google Scholar
18. Birkhoff, G.D. Dynamical systems, 9, AMS Collection Publications, 1972.Google Scholar
19. Leung, A.Y.T. and Ge, T. On the higher order normal form of non linear oscillators, Proc of Int Conf on Vibration Eng, ICVE’94, Beijing, 1994, pp 403408.Google Scholar
20. Chen, Y. and Leung, A.Y.T. Bifurcation and Chaos in Engineering, Springer-verlag Berlin/Heidelberg, 1999.Google Scholar
21. Jinglong, H. and Demao, Z. Normal form and averaging method for non-linear vibration systems (in Chinese), J Vibration Engineering, 1996, 9, (4), pp 371377.Google Scholar
22. Van Der Beek, G.A. Normal form and periodic solutions in the theory of non-linear oscillations existence and asymptotic theory, Int J Non linear Mechanics, 1989, 24, (3), pp 263279.Google Scholar
23. Leung, A.Y.T. and Qichang, Z. Higher-order normal form and period averaging, J Sound and Vibration, 1998.Google Scholar
24. Sedaghat, A., Cooper, J.E., Leung, A.Y.T. and Wright, J.R. Linear Flutter Prediction Using Symbolic Programming, DYMAC99, pp 3743 1999.Google Scholar