CHAOSLIKE PHENOMENA IN THE NONLINEAR DYNAMIC STABILITY OF DISCRETE DAMPED OR UNDAMPED SYSTEMS UNDER STEP LOADING

The non-linear dynamic buckling of a two-degree-of-freedom, damped or undamped, multiple-parameter, structural system under step loading of infinite duration, is thoroughly examined. Attention is mainly focused on the dynamic stability of imperfect multiple-parameter systems which under static loading may either lose their stability through a limit point or exhibit a continuously rising equilibrium path. Considering the stability of motion in the large, in the sense of Lagrange, the dynamic buckling load is defined as the smallest load for which an escape (leading to an unbounded) motion is initiated. A lower bound estimate very close to the exact dynamic buckling load is also established. The discussion of the individual and combined effect on the dynamic buckling load of this autonomous system reveals some interesting phenomena such as: discontinuity in the dynamic buckling load and considerable sensitivity to damping and to initial conditions. Chaoslike and metastability phenomena are also revealed for a simple deterministic system of structural engineering importance.