A Modal Frequency-Domain Generalised Force Matrix for the Unsteady Vortex Lattice Method

The unsteady Vortex Lattice method is becoming an increasingly popular aerodynamic modelling method for incompressible aeroelastic problems, such as flexible low-speed aircraft, wind turbines and flapping flight. It leads to discrete time aeroelastic state space equations, which must be solved in a time-marching framework. Eigenvalue or singular value decompositions of the discrete time equations can be used in order to perform stability analysis but such procedures must be accompanied by model order reduction because the size of the equations is large. This work proposes a modal frequency domain implementation of the Vortex Lattice method, resulting in a modal generalised force matrix. Model order reduction is implicit in the modal approach and stability analysis can be carried out using industry-standard flutter analysis techniques, such as the p-k method. The approach is validated by comparison to wind tunnel flutter data obtained from rectangular cantilever flat plate wings of different aspect ratios and sweep angles. It is found that the aeroelastic model predictions follow the experimental trends for both flutter speed and frequency but tend to be moderately conservative.