The equations of motion for small tethered buoys floating in a nonlinear wave field have been developed. The coupling between rotational and translation3.I degrees of freedom is included in the equations and a three-dimensional response is assumed. The floating buoy is treated as one boundary condition of the governing differential equations for the mooring line coupled buoy-mooring problem.
In this paper the coupling effects of rotational degrees of freedom of tethered floating buoys with the governing equations of the tether are considered. The cable algorithm is described in the following section. The equations of motion for tethered floating buoys in terms of the six degrees of freedom in translation and rotation, which constitute the boundary conditions for one end of the tether, are developed. An algorithm for quasi-linearization of those boundary conditions, which are used in determining the tether motions and buoy rotations for the coupled nonlinear system, is developed and. presented in a subsequent section. Validation of the methodology is provided in the final section. Buoys and their moorings are considered in this work to be classified as small bodies for which the relative-motion Morison equation may be adopted (Sarpkaya and Isaacson, 1981). A coupled analysis is needed for this ocean structure, since the motion of the buoy affects the motion of the mooring and visa versa (Berteaux, 1976).
An iterative algorithm of dynamic analysis of hydrodynamically loaded cable has been developed by Chiou and IISOPE Member Leonard (1991) in which the problem is formulated as a two point boundary value problem. The boundary value problem is then transformed into an iterative set of quasi-linearized boundary value problems, which is then decomposed (Atkinson, 1989) into a set of initial value problems so that spatial integration may be performed along the cable (Sun et al., 1993).
