The three-dimensional nonlinear dynamics of a hanging chain, driven by a large amplitude excitation at the top, are studied numerically and experimentally. Analytic results predict the chain to lose tension over a region adjacent to the free boundary. Numerical results show that large impulselike tension forces cause displacements which lead to a loss of tension and subsequent collapse of the chain. This low-tension behavior is found to be confined to a small region near the free end, while the remaining chain responds like a taut cable. Incorporating bending stiffness is shown to be an effective numerical tool for enforcing the compatibility relations through computationally difficult periods in which the tension vanishes, allowing simulations to continue through the time at which the chain intersects itself. Experimental results were also obtained which confirm qualitatively and quantitatively the numerical predictions. The chain was found to lose tension, collapse, and eventually revert back and intersect itself experimentally as well.
Highly-tensioned chains and cables are used extensively in the offshore industry. There are other applications, however, in which it is desirable to use cables under low tension. For example: neutrally buoyant marine cables supporting hydrophones, either drifting freely or moored loosely, and tethers used for carrying power or communication signals to remotely operated vehicles, particularly when they involve fiber optic lines. In addition, long towed arrays may lose tension during sharp maneuvers, thereby acting as a low-tension cable for periods of time. The term low-tension is used to refer to problems in which the static tension is significantly less than the dynamic tension. The dynamic behavior differs greatly between low-tension and highly tensioned or taut cables. Low-tension problems are particularly complex because the problem cannot be simplified by linearizing the tension, as is typically done for taut cables.
