Some Non-smooth Dynamical Systems in Offshore Mechanics

Examples of vibro-impact mechanical and structural systems in the field of offshore engineering are not uncommon. Various buoyant systems incorporating mooring lines, tethers, rigid bodies, and risers are used for a wide spectrum of purposes, and they often exhibit non-smooth behavior when a characteristic changes abruptly, e.g., when a floating body contacts a rigid harbor, or a slack mooring line becomes taut. However, they present interesting challenges to the analyst and designer trying to predict both their static and dynamic behavior. The environmental conditions in a typical offshore situation naturally lead to stochastic effects, but even in a relatively simple deterministic context, the behavior can still be complicated and somewhat unpredictable. This paper considers two examples drawn from applications in offshore engineering in which a system characteristic (typically stiffness) undergoes a sudden change. They are the motion of a buoyant object restrained by cables, and the rocking of a container on a moving vessel. The primary focus of this paper is to consider relatively simple models, especially the subtle issue of accurately capturing the discrete change in stiffness, and to show the potential for complicated (highly erratic) dynamic behavior. Careful numerical simulation is the primary method of analysis.