On the Application of Liapunov’s Direct Method to Linear Lumped-Parameter Elastic Systems

[+] Author and Article Information
J. A. Walker

Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Ill.

J. Appl. Mech 41(1), 278-284 (Mar 01, 1974) (7 pages) doi:10.1115/1.3423242 History: Received October 01, 1972; Revised March 01, 1973; Online July 12, 2010


A specialized Liapunov functional is presented for stability analysis of linear lumped-parameter elastic systems involving completely general types of forces not explicitly dependent on time. This functional appears to have the simplest possible form capable of providing necessary and sufficient stability conditions for virtually all such systems. Complete analyses are carried out for systems with and without velocity-dependent forces. Simple approaches are given for investigating systems involving “arbitrarily small” and “arbitrarily large” velocity-dependent forces, as well as for determining whether and how the “size” and “structure” of the velocity-dependent forces affect stability. Applications are made to several examples.

Copyright © 1974 by ASME
Topics: Force , Stability
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