Liapunov Functional for a Rectangular, Nonuniform Density Membrane

[+] Author and Article Information
M. W. Dixon

Mechanical Engineering Department, Clemson University, Clemson, S. C.

J. Appl. Mech 40(1), 304-305 (Mar 01, 1973) (2 pages) doi:10.1115/1.3422951 History: Received June 01, 1972; Revised October 01, 1972; Online July 12, 2010


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.

Copyright © 1973 by ASME
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