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 RambergOsgood model. Damage evolution, represented by degradation of the elastic stiffness, is also considered. Analysis results demonstrate behavior that is counterintuitive 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.