Tang, Shijin (2017-05). Dynamic Analysis of Deepwater Multi-Segment Mooring Lines Using Modal Superposition. Master's Thesis.
This thesis starts from the construction of a mathematical model of the multi-segment mooring line, based on the work-energy variational method. The equations of motion in both Cartesian and Lagrange local coordinate systems are derived. Meanwhile, with the catenary theory applied, the static equilibrium configuration of the multi-segment mooring line is determined. Furthermore, Galerkin's finite element method is used to generate mass, stiffness and damping coefficient matrices of a single mooring line. The coefficient matrices in the Lagrange local coordinate system are shown to be diagonal, which means the motions in the three directions of this coordinate system are uncoupled. With this information, the eigenvalue problem is solved to obtain the natural frequencies and associated mode shapes of a mooring line in both coordinate systems. By approximating the mooring line as a linear system, the modal superposition approach allows computationally efficient modeling of dynamics in the frequency domain, including estimation of extreme value statistics using Rice's theory for Gaussian processes. The accuracy of the modal superposition approach is demonstrated through comparison with results from nonlinear time domain simulations using OrcaFlex. This approximate modeling approach is useful for optimizing the design of a mooring system in the preliminary phases of design.