Dynamic Buckling of Autonomous Systems Having Potential Energy Universal Unfoldings of Cuspoid Catastrophe

This work deals with dynamic buckling universal solutions of discrete nondissipative systems under step loading of infinite duration. Attention is focused on total potential energy functions associated with universal unfoldings of cuspoid type catastrophes with one active coordinate. The fold, dual cusp and tilted cusp catastrophes under statically applied loading occurring via limit points, asymmetric/symmetric bifurcations and nondegenerate hysteresis points are extended to the case of dynamic loading. Catastrophe manifolds of these types showing imperfection sensitivity under both types of loading are fully assessed. Important findings regarding dynamic buckling of imperfect systems generated by perfect systems associated with imperfect bifurcations are explored. The analysis is supplemented by a numerical application of a system exhibiting imperfect bifurcation when it is perfect as well as a hysteresis point associated with a tilted cusp catastrophe, when it becomes imperfect.