An Exact Solution for Two-Dimensional Linear Panel Flutter at Supersonic Speeds

O E V E R A L WRITERS HAVE RECENTLY GIVEN attention to the cal^ culation of the flutter behavior of a thin panel, such as occurs in wing, tail, or fuselage coverings. In this type flutter, the basic structure supporting the panel acts essentially as if rigid, while the panel vibrates normal to its own plane. In analyzing the phenomenon, the attempts to date have employed the generalized coordinate approach, using the lower normal modes of the panel as coordinates. In the present note, a theoretically exact solution is deduced for the supersonic flutter of two-dimensional panels of uniform thickness—i.e., uniform plates of infinite width—supported on beams running in the width direction. The supersonic flow is directed normally to the supporting beams and is past one surface of the plate. The fluid on the other side of the plate is stagnant, and it is assumed that its pressure remains sensibly constant. [The flutter of a "flag," with flow past both surfaces of the flag, can be derived from the present results by. multiplying the pressure P(x) by the factor 2.] The present study is restricted to a simply supported panel resting on two rigid beams. However, a straightforward extension of the theory permits taking into account other types of panel end support, beams capable of elastic deflection, and the case of a panel resting on many supports. In practice, the problem of interest is the panel of finite span, rather than the two-dimensional panel. However, it is hoped that the present analysis and its results will throw light on the mechanisms of this new type of flutter and will thus enable an evaluation to be made of the validity of using a Lagrangian approach to the finite-span panel problem, in which only the first few normal panel modes are used as coordinates.