Frequency and Mode Shape Estimates of Marine Catenary Systems using Asymptotic Approximations

The present work highlights some aspects related to the analyses of Arctic offshore floating structures. This thesis consists of five papers, which can be divided into two main categories. One category deals with the dynamics of slender structures with an emphasis on the prediction and suppression of vortex induced vibrations (VIV), and the other category examines the process of interaction between sloping structures and sea ice with focus on developing a numerical model to simulate this process in real time. Slender structures, such as mooring lines and marine risers, are very important for the offshore petroleum industry, which is currently approaching deeper waters. Increasingly, attention has been focused on predicting the susceptibility of these structures to VIV. In this thesis, two asymptotic techniques namely, the local analysis and the WKB methods, were used to derive closed-form solutions for the natural frequencies and mode shapes of slender line-like structures. Both the top-tensioned nearly-vertical configuration and the catenary configuration were considered. The accuracy of the solutions derived was established through comparison with other analytic solution techniques and with results of numerical finite element solutions. The effects of the bending stiffness and the effects of approximating the tension variation as a linear function were discussed. Experimental data on the multi-modal in-line and cross-flow response behaviour of a towed catenary model were analysed to examine the usefulness of the solutions for predicting the response frequencies and envelopes due to VIV. Helical strakes are often used as a mitigating measure to suppress the VIV of slender structures. This thesis presented an innovative method to fit ropes helically to a riser in the installation phase. Such a procedure will help to overcome the handling problem associated with the use of conventional sharp-edged strakes. Experimental investigations were then performed to verify the efficiency of these ropes (round-sectioned helical strakes) in suppressing VIV. Systematic experimental investigations including twenty-eight configurations of round-sectioned helical strakes were tested in an attempt to find the most suitable strake configuration. The effects of varying pitch, the surface roughness and the ratio between the cross-flow and in-line natural frequencies on the efficiency of the proposed configuration of round-sectioned helical strakes were also investigated. The process of interaction between sea ice and offshore sloping structures (e.g., conical structures and ship-shaped structures) is quite complex. Modelling this process is very demanding and often computationally expensive, which typically hinders the chances for realtime simulations. This kind of simulation can be very useful for training personnel for Arctic offshore operations and procedures, for analysing the efficiency of various ice management concepts and as a part of the onboard support systems for station keeping. The challenge of meeting the real-time criterion was overcome in the present work. This thesis developed a numerical model to simulate the process of interaction between sea ice and sloping structures in real time. In this model, only level- and broken-ice features were studied. New analytical closed-form solutions were established and used to represent the ice breaking process. PhysX was used for the first time to solve the equations of rigid body motions with six degrees of freedom for all ice floes in the calculation domain. The results of the simulator were validated against experimental data from model-scale and full-scale tests. Accurate predictions of ice actions are also vital to optimise the design of the structures in the Arctic regions. A good understanding of the role of seawater in the process of interaction between the sloping structures and level ice will help to establish reliable models to estimate the ice forces. This work formulated both the static and dynamic bending problems for a floating wedge-shaped ice beam interacting with an offshore sloping structure. For the dynamic interaction, the effects of the water foundation on the bending failure of the ice were studied by comparing the results of an elastohydrodynamic approach with a model of a Winkler foundation. The thesis also investigated the breaking lengths of the ice wedges (i.e., the frequency of the ice loads) as a function of the ice thickness, the compression in the ice and the acceleration of the interaction.