NONLINEAR DYNAMIC BUCKLING AND STABILITY OF AUTONOMOUS STRUCTURAL SYSTEMS

A general approach for the nonlinear dynamic buckling and stability of dissipative or nondissipative structural systems governed by autonomo us ordinary differential equations (ODEs) is presented. Geometrically imperfect systems with or without symmetric imperfections, as well as statically stable systems, which, in addition to a monotonically risin g (stable) equilibrium path exhibit an unstable complementary path, ar e considered. The role of the dynamic buckling mechanism of the basin of attraction of a stable equilibrium point (on the prebuckling path), as well as the inset (stable) and outset (unstable) manifolds of a sa ddle (on a physical or complementary unstable path), are comprehensive ly explained. A static energy criterion for determining dynamic buckli ng loads for vanishing (but nonzero) damping and lower bound estimates of exact dynamic buckling loads are presented. Metastability, loading discontinuity and chaos-like phenomena are also revealed. The analysi s is supplemented by two illustrative models of practical engineering importance.