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.
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Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation
T. H. Lee,
T. H. Lee
Basic Engineering, Gulf General Atomic, Inc., San Diego, Calif.
C. S. Hsu
Division of Applied Mechanics, University of California, Berkeley, Calif.
Lee, T. H., and Hsu, C. S. (March 1, 1972). "Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation." ASME. J. Appl. Mech. March 1972; 39(1): 244–250. https://doi.org/10.1115/1.3422620
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