| A simply supported two-dimensional panel subjected to supersonic flow is numerically investigated using a Galerkin method, a finite-difference method and a proper orthogonal decomposition method. First-order linear piston theory is used to model the aerodynamic loads, and von Karman plate theory is applied to model the structural non-linearity. The panel is shown to be very rich in dynamics, including stable flat/buckled state, limit cycle oscillation, and chaos. The complexity of the dynamics of the panel is presented in a diagram of stability regions, Lyapunov exponents and two bifurcation diagrams with respect to the in-plane load and the flow velocity. Several new phenomena have been observed, including the co-existence of multiple symmetric limit cycles and the pairing of asymmetric limit cycles. Moreover, reduced order models of the aeroelastic system are constructed by means of proper orthogonal decomposition. The performance of the reduced order models with a striking low dimensionality is tested, and the reduced order models are shown to be accurate and robust for predicting the dynamics of the aeroelastic system. |
