Dynamic Response Of Cables Subject To Ocean Forces
Authors: Meggitt Dallas J. , Webster Ronald L. , Migliore Herman J. 
Published: October 2008

ABSTRACT
This paper reviews current techniques for modeling the response of cable systems subjected to the dynamic effects of the ocean environment. The lumped parameter, finite element, and weighted residual methods are compared in terms of mechanisms for incorporating environmental effects.
Each method is compared for its particular advantages and shortcomings from both numerical and application standpoints. Several examples of applications are given. The methods are compared to themselves and to experimental results for a series of laboratory and ocean experiments.

INTRODUCTION
Cables provide an efficient structural element for structures in which the predominant forces are tensile. Both on land and in the ocean, cable networks have found application to structures which require light-weight, high structural efficiency and large spatial extent. The cable-supported roof in the 1972 Munich Olympic complex is a terrestrial example of a complex cable structure. 1 In the ocean, the need for arrays of oceanographic sensors covering large has placed emphasis on suspended cable structures. The complexity of three-dimensional branched cable networks has required advances in techniques for structural analysis of these structures, particularly for dynamic response. Simple catenary solutions are difficult to apply to branched networks and the wave equation approach is awkward for solving extensively nonlinear problems. As a result, computer-based numerical simulation methods have become the usual approach to analysis of cable systems.
A complete cable system analysis capability should include the following:initial configuration; e.g. steady-state equilibrium under the influence of gravity loads and steady environmental loads;vortex-induced response (" strumming");Nonlinear material behavior, including nonlinear stress-strain behavior, rotational degrees of freedom, and hysteresis effects;Nonlinear geometric effects (large displacement); andNonlinear and stochastic environmental loading
A comprehensive method for analysis of the dynamic response of a cable system would presumably include all of the above; however, experience in analysis of cable systems has shown that the problems of strumming, cable material properties and dynamic cable response can be treated separately. The drag increase due to strumming and the material properties become inputs for the dynamic response calculations.
The reader interested in the calculation of the vortex induced vibration of cables is referred to the summary paper by Griffin, et. al. 3 The virtual drag coefficient determined by the method of Griffin, et a1. 3 can be incorporated in the cable dynamic equations of motion as a modified viscous drag term. Material properties of cables are described in manufacturers' literature and in summary articles.4- 7 For most cable modeling, the effects of permanent deformation due to local kinking, rotational effects, bending stiffness and untwisting of stranded cable are treated as secondary effects. The authors are aware of only a few studies to model generalized cable material behavior. 8- 14

EQUATIONS OF MOTION OF CABLES
The governing equations for the dynamic response of cables have been derived by several investigators. As shown by Breslin15, however, the derivations are essentially equivalent, apart from differences in modeling of environmental forces.