Application of Higher-Order Harmonic Balance to Non-Linear Aeroelastic Systems

Dimitriadis, Grigorios; Vio, Gareth Arthur; Cooper, Jonathan Edward

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Application of Higher-Order Harmonic Balance to Non-Linear Aeroelastic Systems

Dimitriadis, Grigorios; Vio, Gareth Arthur; Cooper, Jonathan Edward

2006 • In Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Keywords :

Nonlinear Aeroelastic Systems; Harmonic Balance; Higher Order Harmonic Balance; Limit Cycle Oscillations

Abstract :

[en] The influence of non-linearities on modern aircrafts is becoming of increasing impor- tance. The ability to accurately characterise LCOs and to predict at which speed they occur is very important. Higher Order Harmonic Balance (HOHB) methods have attracted some interest from the aeroelastic community over the last two decades. Such methods carry the promise of high quality stability prediction and Limit Cycle Oscillation (LCO) amplitude and frequency prediction for non-linear aeroelastic systems. In this paper, a Higher Order Harmonic Balance scheme is devised to extend the effectiveness of the method to systems undergoing secondary Hopf bifurcations. It is shown that the proposed harmonic shifting technique can allow the HOHB method to accurately estimate both branches of limit cycles occurring after the second bifurcation.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale

Vio, Gareth Arthur; University of Manchester > School of Mechanical Aerospace and Civil Engineering

Cooper, Jonathan Edward; University of Manchester > School of Mechanical Aerospace and Civil Engineering

Language :

English

Title :

Application of Higher-Order Harmonic Balance to Non-Linear Aeroelastic Systems

Publication date :

May 2006

Event name :

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Event organizer :

AIAA, ASME, ASCE, AHS, ASC

Event place :

Newport, Rhode Island, United States

Event date :

du 1 mai au 4 mai 2006

Audience :

International

Main work title :

Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Publisher :

AIAA, United States

Pages :

Paper AIAA 2006-2023

Additional URL :

http://pdf.aiaa.org/preview/CDReadyMSDM06_1172/PV2006_2023.pdf

Available on ORBi :

since 30 September 2009

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Bibliography

Vio, G. A. and Cooper, J. E., "Limit Cycle Oscilation Prediction for Aeroelastic Systems with Discrete Bilinear Stiffness," International Journal of Applied Mathematics and Mechanics, Vol. 3, 2005, pp. 100-119.
Ding, Q., Cooper, J. E., and Leung, A. Y. T., "Application of an improved cell mapping method to bilinear stiffness aeroelastic systems," Journal of Fluids and Structures, Vol. 20, No. 1, 2005, pp. 35-49.
Liu, L., Wong, Y. S., and Lee, B. H. K., "Application of the centre manifold theory in non-linear aeroelastlcity," Journal of Sound and Vibration, Vol. 234, No. 4, 1999, pp. 641-659.
Roberts, I., Jones, D. P., Lieven, N. A. J., Bernado, M. D., and Champneys, A. R., "Analysis of piecewise linear aeroelastic systems using numerical continuation," Proceedings of the I MECH E Part G Journal of Aerospace Engineering, Vol. 216, No. 1, 2002, pp. 1-11.
Dimitriadis, G., Vio, G., and Cooper, J., "Stability and LCO Amplitude Prediction For Aeroelastic Systems With Structural And Aerodynamic Nonlinearities Using Numerical Continuation," AVT Symposium on Flow-Induced Unsteady Loads and the Impact on Military Applications, Budapest, Hungary, May 2005.
Liu, L., "Higher Order Harmonic Balance analysis for limit cycle oscillations in an airfoil with cubic restoring forces," Proceedings of the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, Texas, April 2005.
Liu, L. and Dowell, E. H., "The secondary bifurcation of an aeroelastic airfoil motion: effect of higher harmonics," Nonlinear Dynamics, Vol. 37, 2004, pp. 31-49.
Leung, A. Y. T. and Ge, T., "Toeplitz Jacobian matrix for nonlinear periodic vibration," ASME Journal of Applied Mechanics, Vol. 62, 1995, pp. 709-717.
Leung, A. Y. T. and Fung, T. C., "Construction of chaotic regions," Journal of Sound and Vibration, Vol. 131, No. 3, 1989, pp. 445-455.
Tamura, H., Tsuda, Y., and Sueoka, A., "Higher approximation of steady oscillations in nonlinear systems with single degree of freedom," Bulletin of the JSME, Vol. 23, No. 195, 1981, pp. 1616-1624.
Lau, S. L., Cheung, Y. K., and Wu, S. Y., "A variable parameter incrementation method for dynamic instability of linear and nonlinear systems," ASME Journal of Applied Mechanics, Vol. 49, 1982, pp. 849-853.
Lau, S. L., Cheung, Y. K., and Wu, S. Y., "Incremental Harmonic Balance method with multiple time scales for aperiodic vibration of nonlinear systems," ASME Journal of Applied Mechanics, Vol. 50, 1983, pp. 871-876.
Cameron, T. M. and Griffin, J. H., "An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems," ASME Journal of Applied Mechanics, Vol. 56, 1989, pp. 149-153.
Hall, K. C., Thomas, J. P., and Clark, W. S., "Computation of unsteady nonlinear flows in cascades using a Harmonic Balance technique," AIAA Journal, Vol. 40, No. 5, 2002, pp. 879-886.
Thomas, J. P., Dowell, E. H., and Hall, K. C., "Nonlinear inviscid aerodynamic effects on transonic divergence, flutter and limit-cycle oscillations," AIAA Journal, Vol. 40, No. 4, 2002, pp. 638-646.
"Rodden, W. P. and Johnson, E. H., "MSC/NASTRAN Aeroelastic Analysis User's Guide, Version 68," Tech. rep., MSC/NASTRAN, 2004.
Kim, Y. B. and Noah, S. T., "Stability and bifurcation analysis of oscillators with piecewise linear characteristics: a general approach," ASME Journal of Applied Mechanics, Vol. 58, 1991, pp. 545-553.
von Groll, G. and Ewins, D. J., "The harmonic balance method with arc-length continuation in rotor/stator contact problems," Journal of Sound and Vibration, Vol. 241, No. 2, 2001, pp. 223-233.
Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., Aeroelasticity, Dover Publications, New York:, 1996.
Rodden, W. P., Harder, R. L., and Bellinger, E. D., "Aeroelastic additions to NASTRAN," Contractor Report NASA-CR-3094, NASA, 1979.
Eversman, W. and Tewari, A., "Consistent rational-function approximation for unsteady aerodynamics," Journal of Aircraft, Vol. 28, No. 9, 1991, pp. 545-552.
Roger, K. L., "Airplane math modelling methods for active control design," Report AGARD-CP-228, AGARD, 1977.