Nonlinear mode interactions and period-tripling flutter in transonic flow

Near Mach one, the aerodynamic nonlinearities become of first order and can no longer be neglected in flutter calculations. Because the superposition principle also breaks down, aeroelastic modes cannot simply be added in a linear manner, as done in the U g and p-k methods of flutter analysis. This paper discusses two nonlinear phenomena of relevance in transonic flutter analysis and testing: (i) multibranch flutter caused by nonlinear mode interactions, and (ii) the sudden emergence of a fundamentally different nonlinear flutter mode via a period-tripling bifurcation. In the first case, the superposition principle is not valid and flutter may not necessarily occur when the first aeroelastic eigenvalue crosses into the right half-plane. In the second case, the nonlinearities open up a new route to flutter, whereby the reduced frequency of the critical aeroelastic mode is lowered into the unstable range through the period-tripling bifurcation, and an entirely new flutter mode is born. Neither behavior can be understood within the theory of classical linear aeroelasticity. (C) 2004 Published by Elsevier Ltd.