Asymptotic Stability Analysis of Viscoelastic Systems

Abstract

Based on the equivalent energy stability criteria formulated elsewhere by the writer and by others, three approximate techniques are presented herein for the asymptotic stability analysis of the equilibrium of viscoelastic or damped elastic systems subjected to nonconservative and gyroscopic forces. Two of them give sufficient stability loads while the third, which is analogous to the familiar Rayleigh-Ritz method, provides approximate critical loads. It is shown that the Ritz method yields reasonably good results if dissipative (damping) forces are finite. However, further effort must be made to improve the lower bound of the approximate critical loads, which here are shown to be, in general, smaller, or at the most equal to the minimum actual critical load.