Parametric Response Of Tlp Tendons - Theoretical And Numerical Analyses
Authors: Strickland Gordon E. , Mason Alfred B. 
Published: October 2008

Abstract
Under certain conditions TLP anchor lines exhibit vertically excited parametric instabilities. In this paper we first demonstrate how to treat this problem analytically. After an initial treatment of the linearized, undamped problem, to define the instability regions, we then turn to the problem with the inclusion of quadratic hydrodynamic damping. Application of an asymptotic solution procedure yields simple expressions for the finite amplitudes of periodic oscillation in various instability regions.
For an alternative treatment, capable of developing detailed response time histories, we next turn to a numerical analysis of the same structural configurations. Utilizing a suitable finite element computer program, we present a procedure for modeling the quasi-sinusoidal lateral displacements comprising the parametric response. The line is given an initial lateral velocity distribution representing a small perturbation from a straight-line configuration. The long-term steady state amplitudes of oscillations that do not decay to zero represent parametric response amplitudes.
We apply both of these treatments to a representative anchor line configuration and show that they give results that are in excellent agreement. We also discuss additional aspects of the response that are available only from the finite element analysis.

Introduction
In the tension leg platform, or TLP, concept, as illustrated schematically in Figure 1, a large buoyant drilling or production structure is held in place by vertical mooring lines, or tendons, extending downward from each corner of the structure to anchors embedded in the seafloor. In order to provide resistance to horizontal as well as vertical excursions of the structure, the tendons carry a large tensile force, applied to the upper ends of the tendons by the excess buoyancy of the structure. The structure possesses this excess buoyancy by virtue of being drawn downward during the installation process to an operating draft considerably in excess of its free-floating draft.
In addition to the steady state buoyant load, the tendons also experience the oscillating vertical loads imposed on the structure by passing ocean waves and transmitted through it to the tendons. The tendons thus resemble a string in tension where the tension includes a superposed oscillatory component. As is well known, 2 such a string is, under certain conditions, subject to dynamic instability, in which lateral oscillations are induced in the string by the oscillatory component of the axial load. These lateral oscillations can occur even when the magnitude of the oscillating component of the axial load is small compared to the steady state component.
The purpose of the present paper is to determine the conditions under which representative TLP tendons may exhibit dynamic instability, and also to determine the amplitudes of the resulting lateral oscillations when dynamic instability occurs. We will show that these calculations can be carried out analytically, using an asymptotic solution procedure to yield good estimates of the conditions giving instability and of the amplitudes of oscillation. We will also show how these calculations can be carried out numerically using a finite element program.