The Static Stability of a Two-Dimensional Curved Panel in a Supersonic Flow, with an Application to Panel Flutter

Abstract

An elementary analysis is given for the problem of steady-state stability, in a supersonic flow, of a two-dimensional curved panel, hinged at two opposite edges, with the distance between the hinges held fixed. The variation of the panel shape with increasing dynamic pressure of the flow is studied. The existence of a critical supersonic speed of flow, above which it is impossible for a bent panel to maintain static equilibrium, is confirmed. Application of the solution to the panel flutter of a flat panel of supersonic aircraft due to thermal buckling is discussed. The critical dynamic pressure of static instability is an upper bound to that of panel flutter. Since this upper bound approaches zero at the initial stages of thermal buckling, it is concluded that if panel flutter is to be avoided, then, in general, thermal buckling of a flat plate cannot be tolerated.