Modelling the limit cycle oscillations of flat plate wings using inextensible plate theory and the vortex lattice method

A closed form state-space model of the nonlinear aeroelastic response of thin cantilevered flat plates is derived using a combination of Inextensible thin plate theory and a linearized continuous time vortex lattice aerodynamic model. The modal-based model is solved for the amplitude and period of the limit cycles of the flat plates using numerical integration. The resulting predictions are compared to theoretical predictions obtained using Von K´arm´an thin plate theory for an identical flat plate. It is shown that the aeroelastic model predicts the linear flutter conditions and nonlinear response of the plates with reasonable accuracy and the Limit Cycle Oscillation (LCO) amplitude, calculated from the inextensible plate theory, has an initial curvature very similar to the one obtained during of experimental test on similar plates, contrary to the amplitude predictions of the Von-Karman model. This striking feature is very encouraging for future experimental and numerical work.