On the Stability of the Equilibrium of Nonconservative Continuous Systems With Slight Damping

[+] Author and Article Information
S. Nemat-Nasser

Department of the Aerospace and Mechanical Engineering Sciences, University of California at San Diego, La Jolla, Calif.

J. Appl. Mech 34(2), 344-348 (Jun 01, 1967) (5 pages) doi:10.1115/1.3607688 History: Received June 27, 1966; Revised November 10, 1966; Online September 14, 2011


The stability of the equilibrium configuration of a linearly elastic solid (with or without internal damping) subjected to partial follower surface tractions (nonconservative loading) is studied. Proportional loading is considered and it is proved that the flutter (oscillations with increasing amplitude) load parameter of the undamped system is an upper bound for that of the system with slight damping. The necessary and sufficient condition for stability of the equilibrium state with respect to flutter-type motions, and sufficiency conditions for stability with respect to both divergence (or buckling) and flutter, are established. Based on energy considerations, an approximate method of stability analysis is suggested which reduces to the usual energy criterion for the cases of conservative loading.

Copyright © 1967 by ASME
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