Wing Flutter is an endemic instability that limits aircraft speed at any altitude. FAA mandates a 15% safety margin from the Flutter-Boundary. Currently all the work on the problem is Computational-FEM, CFD.
This talk is on the Analytical Theory with Continuum Models. The Wing structure model is a Goland beam allowing for pitch and plunge.
The AeroDynamics is based on the Conservation Laws in Differential Form. Inviscid flow is Characterized by the Euler Full Potential Equation .The Wing Dynamics is shown to be NonLinear Convolution/Evolution in a Hilbert Space. Flutter is an LCO and the Speed is a Hopf Bifurcation Point,determined by the Linearised Model. The aeroelastic modes are eigenvalues of the State Space Stability Operator. A closed form formula is obtained for the Transonic Dip phenomenon. Viscous flow is handled by the Prandtl Boundary Layer Theory, still Under Construction.