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

Abstract

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.