Automatic generation of dynamic models of cables

A new theory for the dynamic modeling of cables is presented in this paper, focusing on underwater applications. The main idea is to approximate the continuous flexibility of the cable by several rigid links connected by fictitious elastic joints, allowing three movements: elevation, azimuth and torsion. The Lagrangian of the system is written in a compact form and can be generated for any number of links chosen to represent the structural dynamics. The application of Euler-Lagrange equations allows to obtain the dynamic model, which in this article was developed analytically for the cases of 2, 3 and 4 links. The dynamic model's equations grow significantly with the growth of the number of links and a detailed analysis of this growth enabled the proposition of generic algorithms for the automatic generation of the vectors and matrices elements, for whatever number of considered links. This theory was proposed considering a cable fixed at one end and free at the other, containing a terminal load. However, it can be easily adapted to flexible structures fixed at both ends and for applications underwater or out of water. The generic algorithms proposed in this article allow fast and automatic retrieval of dynamic models of cables, considering a large number of links to represent the structural flexibility, that would be unfeasible to obtain manually.