Nonlinear dynamics and sensitivity to imperfections in Augusti’s model

The influence of geometric imperfections on the nonlinear behavior and stability of Augusti's model under static and dynamic loads is analyzed. This 2-DOF lumped-parameter system is an archetypal model of modal interaction in stability theory representing a large class of structural problems. When the system displays coincident buckling loads, several postbuckling paths emerge from the bifurcation point (critical load) along the fundamental path, in particular coupled unstable postbuckling paths that control the nonlinear dynamics of the system for load levels lower than the critical load. Systems displaying unstable postbuckling behavior are particularly sensitive to initial imperfections. They decrease the static buckling load and distort the topology of the safe potential well. Herein, coupled/uncoupled dynamic responses, bifurcations, escape from the prebuckling potential well, stability, space-time-varying displacements, and attractor-manifold-basin phase portraits are numerically evaluated with the aim of enlightening the effect of system imperfection sensitivity. In particular, the investigation of the reduction of escape load for several varying system parameters highlights the remarkable loss of safety and dynamic integrity of the structure due to penetration of eroding fractal tongues into the safe basin.