NONLINEAR STABILITY AND DYNAMIC BUCKLING OF AUTONOMOUS DISSIPATIVE SYSTEMS

An analytical approach for the stability and the dynamic buckling response 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 including statically stable systems which display also an unstable complementary path. The significance of the unstable (physical or complementary) path, of the basin of attraction of stable equilibria, and of the insect and outset manifolds of a saddle on the dynamic buckling mechanism is comprehensively examined with the aid of basic theorems of local dynamic analysis. A contradiction between local and global dynamic analysis as well as cases of dynamic buckling with sensitivity to initial conditions and damping, discontinuity and metastability phenomena are also explored. Three simple dissipative systems of structural engineering importance are used as illustrative models.