Flutter Calculations Using the Unsteady Source and Doublet Panel Method

The source and doublet panel method (SDPM) developed by Morino in the 1970s can model unsteady compressible ideal flow around wings and bodies. In this work, the SDPM is adapted to the calculation of aeroelastic solutions for wings. A second-order nonlinear version of Bernoulli’s equation is transformed to the frequency domain and written in terms of the generalized mode shapes and displacements. It is shown that the pressure component at the oscillating frequency is a linear function of the generalized displacements, velocities, and accelerations and can therefore be used to formulate a linear flutter problem. The proposed approach has several advantages over the usual doublet lattice method (DLM) approach: the exact geometry is modeled (including thickness, camber, and twist effects), the motion of the surface can be represented using all six degrees of freedom, the pressure calculation is of higher order, and the aerodynamic mass, damping, and stiffness terms are calculated explicitly. The complete procedure is validated using experimental data from the weakened AGARD 445.6 wing, a NACA 0012 rectangular wing with pitch and plunge degrees of freedom, and an experimental model of a T-tail, yielding flutter predictions that lie closer to the experimental observations than those obtained from the DLM, particularly in the case of the T-tail.