Analytical Studies of Resonances In Taut-Moored Systems

Abstract

ABSTRACT A model is described for the analysis of the dynamics of a surface-floating body moored at sea with a taut, viscoelastic mooring line. The model includes lumped parameter equations for the surface body and distributed parameter equations for the longitudinal and lateral displacements of the mooring line. The method for solution of the system equations, which exhibit boundary condition coupling and coupling through line tension effects, is developed. The longitudinal and lateral dynamics of the system for the case of a "vertical" equilibrium is given particular attention. Maximum resonant line tensions and resonant surface body displacements are computed showing the effects of important system parameters. The results of the study reveal both the conditions under which resonance occurs and the sets of dimensionless parameters which are pertinent to the magnitude of resonant dynamics. The analysis indicates the importance of dynamic design analysis through comparison with static tension predictions. INTRODUCTI ON The selection of a mooring line for the purpose of mooring a surface buoy or platform at sea encompasses the rather involved problem of analyzing the coupled dynamics of the surface body and the mooring line under the forces imposed by sea waves. This problem involves the solution of mixed sets of equations, lumped parameter equations for the surface body and distributed parameter equations for the mooring line. These sets are, furthermore, coupled together through boundary conditions and line tension. It is not unfair to say that, at least in the case of mooring a buoy, a certain amount of cynicism usually accompanies the mooring line selection since it is often felt that the first storm to appear will undoubtedly dismantle the whole thing anyway. However, as industry efforts move to deeper and more remote waters, the need for environmental information and new generations of operational vehicles and platforms will steadily increase the need for more understanding of the dynamics of moored systems. The particular problem of the dynamics of a surface body moored with a single, taut, viscous elastic line will be considered herein. The study has direct application for nylon, Dacron, polypropylene, or natural fiber taut moorings. The viscoelastic characteristic is easily suppressed, however, and the results can easily be applied to taut wire rope moorings. The technique used can also be extended for the analysis of multi-point rather than single-point moorings. The subject of single-point taut moorings has received some, but not extensive, attention in the technical literature. One of the first analytical studies of the viscoelastic character of mooring lines was reported by Paquette and Henderson 1. Much of their data was later used and analyzed by Reid 2 who produced a very thorough analysis of deep sea mooring lines. The oscillation modes of a single deep sea mooring, neglecting line elasticity, were studied by Fofonoff3 with the intention of deriving a means for correcting the measurements of mooring line- mounted current meters. A study having peripheral application to taut mooring problems is the investigation of Goeller and Laura4 concerning packages suspended on elastic lines. The recent publications of Nath5 and Nath and Smith 6 have concentrated on taut moorings, and their beginnings in this area are responsible for the inception of the effort herein. The analysis to be presented differs from past work in that the model used incorporates three degrees-of-freedom of surface body motion along with both the longitudinal and lateral displacement of the mooring line, and the bounda