Flutter and Limit Cycle Oscillations of Cantilevered Plate in Supersonic Flow

Research interest is growing for theoretical models of highly deflected structures in aeroelastic settings. Presented here is a model of a cantilevered plate subjected to axial supersonic flow to determine the flutter boundary and postflutter characteristics of a system such as a trailing edge control surface. The structural model is a nonlinear inextensible beam model with inertia and stiffness geometric nonlinearities, while the aerodynamic model used is both first-order linear and third-order nonlinear Piston Theory with a new geometric modification to account for large deflections of the cantilevered configuration. Comparisons are made between linear and nonlinear structural models as well as linear and nonlinear Piston Theory, with and without this new geometric modification. It is shown that the model is highly sensitive to the inclusion of each nonlinear aerodynamic or structural component and that the new geometric modification to Piston Theory leads to stable limit cycles which otherwise may be unstable. Finally, the use of Piston Theory for these unconventionally large deflections is validated by comparing pressures on the structure to those computed by the Euler equations acting on the structure's prescribed motion.