The study of the tether motion with time-varying length using the absolute nodal coordinate formulation with multiple nonlinear time scales

In this study, the modeling and formulation for tether motion with time-varying length, large rotation, large displacement and large deformation are proposed. A tether or cable is an important element in lift systems, construction machines for transportation and often is used with a time-varying length. In some cases, these systems are large and the tether has a long length, large deformation and large displacement. The dynamic behavior of a tether in extension and retraction using the proposed method is discussed in this paper. In the passage through resonance, significant tether motions with large rotation and large deformation result. In the analysis of this phenomenon, the transient fluctuations of the motion amplitudes are examined and compared with the corresponding steady state motions. The accuracy and the cost of the calculations are also verified by comparison with the experimental results.