LIMIT CYCLE OSCILLATION PREDICTION FOR AEROELASTIC SYSTEMS WITH DISCRETE BILINEAR STIFFNESS

A methodology is presented that enables the prediction of the limit cycle oscillation behaviour of aeroelastic systemscontaining discrete bilinear structural nonlinearitiesusingthe centre manifold and normal form approaches. The approach extends previous work on aeroelastic systems containing discrete cubic structural nonlinearites. A simple fitting technique is developed to approximate the non-linear stiffness behaviour as a polynomial which enables the normal form method to be used. The approach is demonstrated on several binary and multiple degree of freedom simulated non-linear aeroelastic systems. The predicted LCO amplitudes compare well with the numerical integration results and were far superior in comparison to those predicted using the Harmonic Balance method. Limitations of the new approach are discussed.

[1]  Ken Badcock,et al.  Evaluation of methods for the time marching analysis of transonic aeroelasticity , 2001 .

[2]  Jonathan E. Cooper,et al.  Limit cycle oscillation prediction for aeroelastic systems with continuous non-linearities , 2000 .

[3]  P. Chen,et al.  LIMIT-CYCLE-OSCILLATION STUDIES OF A FIGHTER WITH EXTERNAL STORES , 1998 .

[4]  Tanchum Weller,et al.  Poincaré-like Simple Cell Mapping For Non-linear Dynamical Systems , 1994 .

[5]  S. Shen.  An Approximate Analysis of Nonlinear Flutter Problems , 1959 .

[6]  E. Dowell,et al.  Nonlinear Behavior of a Typical Airfoil Section with Control Surface Freeplay: a Numerical and Experimental Study , 1997 .

[7]  Andrew J. Kurdila,et al.  Identification and Control of Limit Cycle Oscillations in Aeroelastic Systems , 1999 .

[8]  C. L. Lee.  An Iterative Procedure for Nonlinear Flutter Analysis , 1986 .

[9]  Jonathan E. Cooper,et al.  Limit Cycle Oscillation Control and Suppression , 1999 .

[10]  Zhichun Yang,et al.  Analysis of limit cycle flutter of an airfoil in incompressible flow , 1988 .

[11]  Jonathan E. Cooper,et al.  Application of an improved cell mapping method to bilinear stiffness aeroelastic systems , 2005 .

[12]  G. J. Hancock,et al.  On the teaching of the principles of wing flexure-torsion flutter , 1985 .

[13]  Chen Yushu,et al.  Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing's Equation , 1994 .

[14]  Jonathan E. Cooper,et al.  ESTIMATION OF THE HOPF BIFURCATION POINT FOR AEROELASTIC SYSTEMS , 2001 .

[15]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[16]  Stuart J. Price,et al.  THE AEROELASTIC RESPONSE OF A TWO-DIMENSIONAL AIRFOIL WITH BILINEAR AND CUBIC STRUCTURAL NONLINEARITIES , 1995 .

[17]  Carlos E. S. Cesnik,et al.  Aeroelastic response of multi-segmented hinged wings , 2001 .

[18]  A. Leung,et al.  An Algorithm for Higher Order Hopf Normal Forms , 1995 .

[19]  Andrew Y. T. Leung,et al.  HIGHER ORDER NORMAL FORM AND PERIOD AVERAGING , 1998 .

[20]  S. J. Price,et al.  NONLINEAR AEROELASTIC ANALYSIS OF AIRFOILS : BIFURCATION AND CHAOS , 1999 .

[21]  E. Dowell,et al.  Limit cycle behavior of an airfoil with a control surface , 1998 .

[22]  Grigorios Dimitriadis,et al.  Characterization of nonlinear aeroservoelastic behaviour , 1999 .

[23]  Earl H. Dowell,et al.  On the evolution of deterministic non-periodic behavior of an airfoil , 1999 .