Finite-Element Panel Flutter in Three-Dimensional Supersonic Unsteady Potential Flow

A finite-element formulation and solution procedure are developed for flutter prediction of rectangular panels with one surface exposed to three-dimensi onal supersonic unsteady potential flow. Each element is divided into several Mach boxes. The aerodynamic influence coefficients between each pair of sending and receiving boxes are computed by the method of Gaussian quadrature. The aerodynamic matrix is based on the numerically computed velocity potentials for all boxes. The effect of in-plane force is included. This development is particularly useful in the low supersonic range for panels with chord-span ratio less than about one, where the piston theory does not give satisfactory accuracy. Examples are demonstrated by using the 16 d.o.f. rectangular plate element. Results for flutter boundaries for the unstressed panels agree well with an alternative Galerkin's modal solution. The examples demonstrate that flutter boundaries are dominated by higher modes for panels with higher chord-span ratio. They also demonstrate that the dominating flutter boundaries abruptly change modes as the Mach number is varied. The beneficial effect of in-plane tension is demonstrated.