Abstract
Hopf-bifurcation analysis is used to determine the nutter boundaries of a pitch and plunge airfoil with a flap at transonic Mach number conditions. The nonlinear pitch, plunge, and flap airfoil model is a coupling of the Euler equations and a three degree-offreedom structural model composed of linear and torsional springs. The Euler equations are discretized using an upwind total variation diminishing scheme of Harten and Yee. Equilibrium solutions of the structural coupling model are computed using the fully implicit Newton's method; dynamic solutions are computed explicitly. The grid about the deformed shape of the airfoil/flap configuration is modified with a shearing method. The Hopf-bifurcation point, which models the flutter condition, is computed using a modified form of the Griewank and Reddien algorithm. Paths of Hopf points are computed as functions of the freestream Mach number to determine the flutter boundary. The flutter boundary is validated by time-integration of the structural coupling model and comparison to solutions in the literature.
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