Liapunov Functional for a Rectangular, Nonuniform Density Membrane

Abstract

The question of stability of equilibrium of a general rectangular, nonuniform density membrane adjacent to a supersonic airstream arbitrarily directed with respect to the edges of the membrane is considered using the direct method of Liapunov. The governing equation of the system, derived using piston theory, is used with the developed Liapunov functional to show that the equilibrium of the system is stable in the absence of structural damping, or for structural damping of a certain form.