Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation

[+] Author and Article Information
T. H. Lee

Basic Engineering, Gulf General Atomic, Inc., San Diego, Calif.

C. S. Hsu

Division of Applied Mechanics, University of California, Berkeley, Calif.

J. Appl. Mech 39(1), 244-250 (Mar 01, 1972) (7 pages) doi:10.1115/1.3422620 History: Received September 09, 1970; Revised March 08, 1971; Online July 12, 2010


A Liapunov direct method is developed here to derive stability criteria for continuous systems under parametric excitation. The method makes use of time-dependent Liapunov functionals and the extremal properties of Rayleigh quotients of self-adjoint operators. The application of the method entails solving an eigenvalue problem with the variable t appearing in the problem strictly as a parameter. As examples of application the method is applied to (a) a clamped column under the action of periodic axial load, and (b) the panel flutter problem with the panel also subjected to periodic in-plane load. The calculated results for the first example show improvement over those obtained previously.

Copyright © 1972 by ASME
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