Influence of aerodynamic nonlinearity due to static panel-curvature on flutter of panels at transonic and low supersonic Mach numbers

This study focuses on assessing the influence of aerodynamic nonlinearity due to a static panel curvature on the flutter characteristics of a semi-infinite panel at transonic and low supersonic Mach numbers. The fluid flow is modeled with compressible Euler equations and discretized using density-based streamline-upwind Petrov Galerkin finite element variational form. The structure is analyzed using finite element discretization of a linear Timoshenko beam model. The curved shape of the panel is defined by a half-sine bump with increasing amplitude. Steady-state flow is calculated for this shape and a linearization about this state is used to solve for the flutter mode using a small-disturbance stability eigenvalue formulation. The flutter characteristics are studied for increasing height of the panel curve at several Mach numbers between 0.7 and 2.0. At subsonic Mach numbers flow over the curved panel creates a supersonic bubble and at a sufficiently large height changes the instability mode from zero-frequency divergence to oscillatory flutter. At low supersonic Mach numbers the increasing curve height creates a subsonic region over the panel with a change in the composition of the resulting flutter mode. While the flutter speed is seen to monotonically increase at Mach 1.1, large reductions are observed at Mach 1.5 and 2.0.