Abstract
A general approach for the nonlinear dynamic buckling and stability of dissipative or nondissipative structural systems governed by autonomous 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 rising (stable) equilibrium path exhibit an unstable complementary path, are 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 saddle (on a physical or complementary unstable path), are comprehensively explained. A static energy criterion for determining dynamic buckling 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 analysis is supplemented by two illustrative models of practical engineering importance.
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