Literature Review : LYAPUNOV STABILITY CRITERIA FOR CONTINUOUS SYSTEMS UNDER PARAMETRIC EXCITATION Lee, T. H. and Hsu, C. S. J. Appl. Mech. , Trans. ASME 39(1), 244-250 (Mar. 1972) 11 refs Refer to Abstract No. 72-1595

1973 ◽  
Vol 5 (4) ◽  
pp. 60-61
Author(s):  
J.A. Walker
Keyword(s):  
Literature Review ◽  
Lyapunov Stability ◽  
Parametric Excitation ◽  
Continuous Systems ◽  
Stability Criteria ◽  
Lyapunov Stability Criteria ◽  
Trans Asme

Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation

1972 ◽  
Vol 39 (1) ◽  
pp. 244-250 ◽  
Author(s):  
T. H. Lee ◽  
C. S. Hsu
Keyword(s):  
Parametric Excitation ◽  
Direct Method ◽  
Continuous Systems ◽  
Panel Flutter ◽  
Stability Criteria ◽  
Use Of Time ◽  
Liapunov Direct Method ◽  
Liapunov Functionals ◽  
Adjoint Operators ◽  
Extremal Properties

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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