galloping; aeroelasticity; harmonic balance; normal form; numerical continuation; cell mapping; centre manifold
Abstract :
[en] A global stability and bifurcation analysis of the transverse galloping of a square section beam in a normal steady flow has been implemented. The model is an ordinary differential equation with polynomial damping nonlinearity. Six methods are used to predict bifurcation, the amplitudes and periods of the ensuing Limit Cycle Oscillations: (i) Cell mapping, {ii} Harmonic Balance, (iii) Higher Order Harmonic Balance,(iv) Centre Manifold linearization, (v) Normal Form and (vi) Numerical Continuation. The resulting stability predictions are compared with each other and with results obtained from numerical integration. The advantages and disadvantages of each technique are discussed. It is shown that, despite the simplicity of the system, only two of the methods succeed in predicting its full response spectrum. These are Higher Order Harmonic Balance and Numerical Continuation.
Vio, Gareth Arthur; University of Liverpool > Department of Engineering
Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Intéractions fluide structure et aérodynamique expérimentale
Cooper, Jonathan E; University of Liverpool > Department of Engineering
Language :
English
Title :
Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem
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Bibliography
Allgower E.L., and Georg K. Numerical Continuation Methods: An Introduction (1990), Springer, New York
Attar P.J., Dowell E.H., and White J.R. Modeling delta wing limit-cycle oscillations using a high-fidelity structural model. Journal of Aircraft 42 (2005) 1209-1217
Badcock K.J., Woodgate M.A., and Richards B.E. Direct aeroelastic bifurcation analysis of a symmetric wing based on Euler equations. Journal of Aircraft 42 (2005) 731-737
Bearman P., and Luo S. Investigation of the aerodynamic instability by forced oscillation. Journal of Fluids and Structures 2 (1988) 161-176
Bearman P.W., and Luo S.C. Experiments on flow induced vibration of a square-section cylinder. Journal of Fluids and Structures 1 (1987) 19-34
Beyn W.-J., Champneys A., Doedel E., Govaerts W., Kuznetsov Y.A., and Sandstede B. Numerical continuation and computation of normal forms. In: Fiedler B. (Ed). Handbook of Dynamical Systems vol. 2 (2002), Elsevier, Amsterdam
Blevins R.D. Flow Induced Vibration (1990), Van Nostrand Reinhold, New York
Cameron T.M., and Griffin J.H. An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. Journal of Applied Mechanics 56 (1989) 149-153
Carr J. Application of Centre Manifold Theory (1981), Springer, Berlin
Chen Y., and Leung A.Y.T. Bifurcation and Chaos in Engineering (1998), Springer, Berlin
Conner M.D., Tang D.M., Dowell E.H., and Virgin L. Nonlinear behaviour of a typical airfoil section with control surface freeplay: a numerical and experimental study. Journal of Fluids and Structures 11 (1997) 89-109
Dimitriadis G., and Cooper J.E. Characterization of the behaviour of a simple aeroservoelastic system with control nonlinearities. Journal of Fluids and Structures 14 (2000) 1173-1193
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 (May 2005), Budapest, Hungary
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 20 (2005) 35-49
Dormand J.R., and Prince P.J. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6 (1980) 19-26
In: Dowell E.H. (Ed). A Modern Course in Aeroelasticity. fourth ed. (2004), Kluwer Academic Publishers, Dordrecht
Fairgrieve, T.F., 1994. The computation and use of Floquet multipliers for bifurcation. Ph.D. Thesis, University of Toronto, Canada.
Garcia J.A. Numerical investigation of nonlinear aeroelastic effects on flexible high-aspect-ratio wings. Journal of Aircraft 42 (2005) 1025-1036
Girodroux-Lavigne P., and Dugeai A. Transonic aeroelastic computations using Navier-Stokes equations. Proceedings of the CEAS International Forum on Aeroelasticity and Structural Dynamics (2003), Amsterdam, The Netherlands
Govaerts W., Dhooge A., and Kuznetsov Y.A. MATCONT: a Matlab package for numerical bifurcation of ODES. ACM Transactions on Mathematical Software 29 (2003) 141-164
Hsu C. Cell-to-Cell Mapping (1987), Springer, New York
Kholodar D.B., Dowell E.H., Thomas J.P., and Hall K.C. Limit-cycle oscillations of a typical airfoil in transonic flow. Journal of Aircraft 41 (2004) 1067-1072
Kim D.-H., Lee I., Marzocca P., Librescu L., and Schober S. Nonlinear aeroelastic analysis of an airfoil using CFD-based indicial approach. Journal of Aircraft 42 (2005) 1340-1343
Kuznetsov, Y., Levitin, V., 1997. CONTENT: integrated environment for analysis of dynamical systems. Technical Report, Centrum voor Wiskunde en Informatica, Amsterdam.
Kuznetsov Y.A. Elements of Applied Bifurcation Theory (1998), Springer, New York
Lau S.L., Cheung Y.K., and Wu S.Y. A variable parameter incrementation method for dynamic instability of linear and nonlinear systems. Journal of Applied Mechanics 49 (1982) 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. Journal of Applied Mechanics 50 (1983) 871-876
Lee B.H.K., Liu L., and Chung K.W. Airfoil motion in subsonic flow with strong cubic restoring forces. Journal of Sound and Vibration 281 (2005) 699-717
Lee C.L. An iterative procedure for nonlinear flutter analysis. AIAA Journal 24 (1986) 833-840
Leung A.Y.T., and Chui S.K. Non-linear vibration of coupled Duffing oscillators by an improved incremental harmonic balance method. Journal of Sound and Vibration 181 (1995) 619-633
Leung A.Y.T., and Qichang Z. Higher order normal form and period averaging. Journal of Sound and Vibration 217 (1998) 795-806
Levitas J., and Weller T. Poincaré linear interpolated cell mapping: method for global analysis of oscillating systems. Journal of Applied Mechanics 62 (1995) 489-495
Liu, L., 2005. Higher order harmonic balance analysis for limit cycle oscillations in an airfoil with cubic restoring forces. In: Proceedings of the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, Texas, April.
Liu L., Wong Y.S., and Lee B.H.K. Application of the centre manifold theory in non-linear aeroelasticity. Journal of Sound and Vibration 234 (1999) 641-659
Luo S.C., Chew Y.T., and Ng Y.T. Hysteresis phenomenon in the galloping oscillation of a square cylinder. Journal of Fluids and Structures 18 (2003) 103-118
McIntosh Jr. S.C., Reed R.E., and Rodden W.P. Experimental and theoretical study of nonlinear flutter. Journal of Aircraft 18 (1981) 1057-1063
Nam, C., Chen, P.C., Liu, D.D., Urnes, R., Yurkovich, R., 2001. Adaptive reconfigurable control of F/A-18 stores limit cycle oscillations. In: Proceedings of the CEAS International Forum on Aeroelasticity and Structural Dynamics, Madrid, Spain, June.
Nayfeh A.H. Methods of Normal Forms (1993), Wiley, New York
Norberg C. Flow around rectangular cylinders-pressure and wake frequencies. Journal of Wind Engineering and Industrial Aerodynamics 49 (1993) 187-196
Parkinson G. Phenomena and modelling of flow-induced vibrations of bluff bodies. Progress in Aerospace Sciences 26 (1989) 169-224
Parkinson P., and Brooks N.P.H. On the aeroelastic instability of bluff cylinders. Journal of Applied Mechanics 28 (1961) 252-258
Parkinson P., and Smith J.D. The square prism as an aeroelastic non-linear oscillator. Quarterly Journal of Mathematical and Applied Mathematics 17 (1964) 225-239
Patil M.J., Hodges D.H., and Cesnik C.E.S. Limit cycle oscillations in high-aspect-ratio wings. Journal of Fluids and Structures 15 (2001) 107-132
Price S.J., Alighanbari H., and Lee B.H.K. The aeroelastic behaviour of a two-dimensional airfoil with bilinear and cubic structural nonlinearities. Journal of Fluids and Structures 9 (1995) 175-193
Raghothama A., and Narayanan S. Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method. Journal of Sound and Vibration 226 (1999) 493-517
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 IMechE Part G: Journal of Aerospace Engineering 216 (2002) 1-11
Scruton, C., 1960. The use of wind tunnel in industrial research. Report 309, AGARD.
Simiu E., and Scanlan R.H. Wind Effect on Structures: Fundamentals and Applications to Design (1996), Wiley, New York
Strogatz S.H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (1994), Perseus Books, Cambridge, MA
Tamura H., Tsuda Y., and Sueoka A. Higher approximation of steady oscillations in nonlinear systems with single degree of freedom. Bulletin of the JSME 23 (1981) 1616-1624
Thomas J.P., Dowell E.H., and Hall K.C. Modeling viscous transonic limit-cycle oscillation behavior using a harmonic balance approach. Journal of Aircraft 41 (2004) 1266-1274
Verhulst F. Nonlinear Differential Equations and Dynamical Systems. second ed. (1996), Springer, Berlin
Vio G.A., and Cooper J.E. Limit cycle oscillation prediction for aeroelastic systems with discrete bilinear stiffness. International Journal of Applied Mathematics and Mechanics 3 (2005) 100-119
Woodgate M.A., Badcock K.J., Rampurawala A.M., Richards B.E., Nardini D., and Henshaw M.J.deC. Direct aeroelastic bifurcation analysis of a symmetric wing based on Euler equations. Journal of Aircraft 42 (2005) 1005-1012
Yang Z.C., and Zhao L.C. Analysis of limit cycle flutter of an airfoil in incompressible flow. Journal of Sound and Vibration 123 (1988) 1-13
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