NONLINEAR STABILITY AND DYNAMIC BUCKLING OF AUTONOMOUS DISSIPATIVE SYSTEMS

An analytical approach for the stability and the dynamic buckling resp onse of multiple-parameter dissipative systems described by autonomous differential equations is presented. Attention is focused on general imperfect structural systems with or without symmetric imperfections i ncluding statically stable systems which display also an unstable comp lementary path. The significance of the unstable (physical or compleme ntary) path, of the basin of attraction of stable equilibria, and of t he insect and outset manifolds of a saddle on the dynamic buckling mec hanism is comprehensively examined with the aid of basic theorems of l ocal dynamic analysis. A contradiction between local and global dynami c analysis as well as cases of dynamic buckling with sensitivity to in itial conditions and damping, discontinuity and metastability phenomen a are also explored. Three simple dissipative systems of structural en gineering importance are used as illustrative models.