The stability of equilibrium of an arbitrarily shaped, multiply connected, nonuniform-density, plane membrane adjacent to a supersonic airstream is studied using the direct method of Liapunov. In the piston theory regime it is found that plane membranes cannot flutter in the absence of structural damping, regardless of shape or mass distribution. Linear and nonlinear structural damping are then studied and the possibility of destabilization by damping is noted. Means of extending the present analysis to cover the effects of small nonlinearities and time-varying parameters are also discussed.

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