Nonlinear dynamics of a harmonically-excited inelastic inverted pendulum

Issues of dynamic stability for a single-degree-of-freedom system subjected to a time-varying axial load are presented. The linearized differential equation of motion for the model structure is given by the well-known Mathieu equation. Parametric resonance leading to dynamic instability is known to occur for such a system. This paper examines the response of the geometrically exact model for two inelastic constitutive models-an elastic-perfectly plastic model and a cyclic Ramberg-Osgood model. Damage evolution, represented by degradation of the elastic stiffness, is also considered. Analysis results demonstrate behavior that is counter-intuitive to what would be expected under static or monotonic loading conditions. Though simple, this structural model helps illustrate the complex features in the response of an inelastic dynamical system.