An. Kounadis, NONLINEAR DYNAMIC BUCKLING AND STABILITY OF AUTONOMOUS STRUCTURAL SYSTEMS, International journal of mechanical sciences, 35(8), 1993, pp. 643-656
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.