Dynamic ratcheting in elastoplastic single-degree-of-freedom systems

In dynamic analysis, hysteretic damping often provides a reasonable model of the inelastic behavior of a structure. Nonlinearity presented by hysteretic damping, however, introduces the possibility of developing complicated motions not expected in linear dynamics. In this study, motions of a single-degree-of-freedom system with hysteretic damping under dual-frequency sinusoidal excitations are investigated through numerical simulation. Hysteretic damping behavior is represented by three different plasticity models: the elasto-perfectly-plastic model; the linear kinematic hardening model; and the two-surface model. Under certain conditions, the resultant motions from the elasto-perfectly-plastic model and the two-surface model exhibit a continual increment of plastic deformation in successive cycles. Parametric study shows that this dynamic ratcheting develops when applied frequencies are commensurable (i.e., related to each other with integer ratio), and the product of terms comprising the ratio is an even number. In the Poincaré section, motion from commensurable frequencies shows limit cycle behavior, whereas the boundedness of motion for incommensurable frequencies is depicted by having quasi-periodicity. On the other hand, the response of the linear kinematic hardening model is qualitatively different and, in particular, dynamic ratcheting does not develop, irrespective of the frequency commensurability. These findings suggest that model selection may have unanticipated consequences for the analysis and design of structural systems subjected to severe dynamic loadings, such as major earthquakes.