Tension In A Taut Line Mooring; Frequency Domain Analysis
Authors: Hong S.T. 
Published: October 2008

ABSTRACT
The random response of a taut line mooring excited by sea waves is treated in this paper. For analytical convenience, mooring line tension is divided into a deterministic quasi-static component and a random dynamic component. Since the dynamic component is random, the total mooring line tension is also a random quantity and is described by a statistical function.
Response spectra of the dynamic mooring line tension, and other response quantities, are obtained in frequency domain based on a liberalized structural model and a stationary erotic, Gaussian sea state.
For a typical deep-sea taut mooring in 10,000 ft of water, the dynamic tension is only a small fraction of the quasi-static tension, and the maximum dynamic tension is found to be at the top of the mooring line. The longitudinal hydrodynamic dragon-the rope surface is shown to be the predominant damping source. It appears that resonance would not be a problem for the design of a deep-sea taut mooring.
The analytical tool developed here may be used as a design aid in determining the optimum rope combination, rope construction, rope size, and anchor weight.

INTRODUCTION
The feasibility of using a buoy network as a tool for collecting marine environmental data has been well recognized. 1 Because excessive buoy excursion and mooring line inclination are not permissible for data-collecting purposes, a single point taut mooring appears to be a suitable choice for anchoring the instrumentation buoy in the open ocean. The dynamic behavior of such a mooring system in a random sea must be understood before a reliable buoy network can be established.
A time-domain analysis appears to be the most suitable for simulating the dynamic response of a mooring line in a random sea state since several types of nonlinearities, such as loading, geometry, and material, are involved in the governing equations. By using random waves as the excitation to the buoy system, the time histories of the response quantities (e.g., displacement, stress and strain at any point of the mooring line) may be obtained. Statistical properties of the response quantities can thus be derived from the time histories. However, each of the steps, i.e., wave simulation, dynamic analysis and statistical analysis, involves extensive computer time. The high cost and special knowledge required by this method may make it too expensive for normal design use.
In light of the difficulties encountered in a complete time-domain analysis, it became necessary to search for an analytical solution in the frequency domain in order that the dynamic response of a buoy system in a random sea can be obtained in a reasonable amount of computer time. Such a solution is presented in this paper. In essence, a set of one-dimensional linear wave equations is formulated based on a liberalized structural model. The equations are solved to obtain the frequency response functions at various frequencies. The response spectrum of the dynamic tension is then computed from the wave spectrum and the frequency response functions. The variance of the dynamic tension can be obtained by integrating the response spectrum.