ABSTRACT

A unified solution to the linear dynamics of inclined marine cables is presented and the effect of the principal parameters, including cable elasticity, local curvature, and tension and mass distribution are analyzed in detail. A numerical scheme using the linear solutions to construct a solution for the nonlinear problem is discussed.

INTRODUCTION

Wire and cable dynamics is an old subject, with analytic solutions dating back to the 18th century. The recent move towards deeper water in the offshore industry made mooring systems very attractive and created interest in the dynamics of such systems

The first step is to determine whether the natural frequencies of a mooring line are within the frequency range of the exciting waves. An important finding, related to this procedure, is that the natural modes that are symmetric (or quasi-symmetric) with respect to a plane perpendicular to the cable configuration at the midlength point (for example the first mode of a taut wire) involve large dynamic tensions, while the antisymmetric modes do not.

In this paper a number of recently derived analytic solutions for the linear cable dynamics are presented and then used to determine the effect of the most crucial parameters. Finally, a number of figures to determine the natural frequencies are prepared, based on those solutions for design applications.

The authors will not make the usual excuses for using a linear analysis to an admittedly nonlinear problem: The linear solutions provided herein can be used to construct a very efficient nonlinear solution algorithm, as briefly described in the present paper.

CABLE DYNAMICS

The in-plane dynamics of a cable whose static, solution lies entirely in a vertical plane will be considered. The out of plane dynamics are easier and are discussed in the end.

GOVERNING EQUATIONS

We consider a cable whose unstretched area is Ao diameter do mass per unit length mo and Young's modulus E.

Let s denote the unstretched Lagrangian coordinate from an arbitrary origin (usually the bottom end of the cable) to a material point of the cable, and p the corresponding stretched coordinate.

The cable is immersed in water, the hydrostatic pressure by defining tension T e as:

  • (Equation Available In Full Paper)

where T is the tension at a point of the cable, P is the hydrostatic pressure at the same point and A fhe stretched cable area. Then the weight of the cable pel unit length is:

  • (Equation Available In Full Paper)

where m is the stretched mass per unit length and the water density. We assume in this paper that Poisson's ratio is 1/2 so that if e is the longitudinal strain then by applying the generalized Hooke's law we obtain [1]:

Keywords:
antoine shek, dynamic tension, unit length, atc 4498, natural frequency, frequency, cable dynamic, mode crossover, cable, configuration
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