Simulation models for the dynamic vibrations of a suspended cable with a sliding bead

The single point bead moving along a slack statically suspended catenary-cable presents a prototype example for the dynamic interaction of moving inertial loads with flexible structures. Depending on the particular choice of problem parameters it may be seen as a simplistic mechanical model to mimic cable car or pantograph-catenary dynamics. Here, it serves as an academic benchmark problem to perform a comparative study of different numerical simulation approaches ranging from reduced flexible multi-body models to structural finite element implementations in conventional Lagrangian and advanced mixed Eulerian--Lagrangian parametrisation. In the spirit of the so-called sliding rod formulation, the latter utilizes an alternative parametrisation of the material volume with non-material axial coordinates that allows for an automatic mesh-adjustment to the actual bead position. Thus, spurious numerical phenomena induced by the bead motion across material boundaries are avoided, which presents a major difficulty for the conventional models due to the inherent lumping of the inertial interaction. Potential model extensions for the future are the account for friction, multi-bead interaction or elastic suspensions as well as the incorporation of active motion-control or modifications to accurately capture moving inertial loads across spatially fixed supports. Presently, the comparatively simple single bead example is considered in a series of transient simulation tests to assess the capabilities and convergence behavior of the numerical models in different dynamic vibration scenarios with taut and slack cable.