Eigenvalue Based Fast Flutter Method

The flutter prediction problem can be formulated as a Hopf Bifurcation prediction for an equilibrium of a steady state of the semi-discrete system of ODE's. When looked at in this way we can attempt to track the critical eigenvalue of the coupled system Jacobian matrix, inferring loss of stability when an eigenvalue pair crosses the imaginary axis. This can be done in a number of ways, but we have managed to demonstrate unique methods in 3D. Technicalities have included forming the Jacobian matrices and solving the large sparse system of equations in parallel. The punchline for this work is that flutter points can be calculated in a CPU time equivalent to 1 steady to 1 unsteady calculation. The influence of the aeroelastic solution (often for transonic problems critical) is fully accounted for, in contrast to several POD and system ID methods.

Publications

1. Badcock, K.J., Woodgate, M.A. and Richards, B.E., Hopf Bifurcation Calculations for a Symmetric Aerofoil in Transonic Flow, AIAA Journal, pp883-892, vol 42 no 5, May 2004.
2. Badcock, K.J., Woodgate, M.A. and Richards, B.E., Direct Aeroelastic Bifurcation Analysis of a Symmetric Wing Based on the Euler Equations, Journal of Aircraft, Vol 42, No 3, pp731-737, 2005.
3. Woodgate M.A., and Badcock, K.J., Fast prediction of Transonic Aeroelastic Stability and Limit Cycles. AIAA Journal, 45(6),1370-1381,2007.

Contact: Mark Woodgate