On the dynamics of low tension marine cables
This thesis is concerned with the dynamics of low tension marine cables. These cables are widely used in the ocean environment for signal and power transmission applications. There are two main issues in the dynamic analysis of such cables. When the tension is zero, which is often the situation encountered at the seabed during cable laying, the cable geometric stiffness matrix becomes singular. The other issue is that the transformation from local co-ordinates to global co-ordinates made through Euler angles leads to a greater number of unknowns than the number of differential equations. The former problem can be overcome by taking into account the flexural rigidity of the cable. The latter problem can be overcome by assuming that one of the Euler angles is known. However, this procedure can introduce singularities on the formulation of the problem. A new three dimensional model for the dynamics of marine cables is presented in this thesis. The model takes into account the bending stiffness of the cable in order to overcome singularities in the geometric stiffness matrix. In order to overcome the problem owing to the use of Euler angles, a new displacement approach is introduced. This new displacement approach uses the differential geometry definition of curvature and torsion in order to establish the transformation from the local co-ordinates to the global co-ordinates. The general formulation of the dynamics of marine cables presented in this thesis is applicable to a wide range of cases such as towed cables, cable installation and cable recovery. In order to illustrate this new formulation the cases of towed cables and cable installation are investigated in the some detail. Solutions for the differential equations of motion are presented for two and three dimensions. The two dimensional solution is obtained through a finite element based technique which uses a weak Galerkin formulation for integration in space and the Newmark method for integration in time. The model's results are compared with full scale measurements. Simulations of the dynamic response of marine cables to vessel wave induced motions and vessel changes in speed are also presented. The three dimensional solution is obtained by expressing the equations of motion as functions of the Euler angles. The space integration is also performed by a finite element model but it uses a finite difference scheme for the time integration. This solution is then used to study the influence of sheared cross-currents in the cable's configuration. Finally, conclusions and suggestions for further research are presented.