Marine Cables Research Articles

The transient behaviour of marine cables being laid—the two-dimensional problem

This paper presents a numerical model for the transient behaviour of marine cables during laying operations. The solution methodology consists of dividing the cable into n straight elements with equilibrium relationships and geometric compatibility equations satisfied for each element. The system of n non-linear ordinary differential equations is then solved by fourth- and fifth-order Runge-Kutta formulae. Results are presented for the cable element slope, cable-top tension, suspended length and required pay-out rate as functions of time and for the cable configuration when the cable ship accelerates or decelerates rectilinearly. The results indicate the necessity of considering the cable dynamics in such analyses, particularly for high cable laying speeds.

Transient behaviour of towed marine cables in two dimensions

This paper presents a numerical solution for the transient motion of marine cables being towed from a cable ship which is changing speed. The cable ship is assumed to move rectilinearly, hence the cable configuration is two-dimensional. The solution methodology consists of dividing the cable into n straight elements with equilibrium relationships and geometric compatibility equations satisfied in each element. A system of n non-linear ordinary differential equations is derived from this and then solved by fourth- and fifth-order Runge—Kutta formulations with the dynamic axial tension calculated iteratively because it is itself dependent on the solution. Results are presented for the cable-top tension and element angles as functions of time and for transient cable geometries when the towing velocity is linearly or parabolically increased (or decreased). It is shown that the results from this analysis compare reasonably well with full-scale experimental data from Hopland (Proc. Int. Wire and Cable Symp., 1993, pp. 734–39).

Rotary bending of marine cables and umbilicals

The stress analysis of a marine cable or umbilical in a rotary bending test rig is presented. It is shown that the finite length of the test sample and the terminations have a significant influence on the stresses in the umbilical which is taken into consideration in determining the cyclic stress distribution in the helical components. Consistency between the theory and test results is demonstrated.

Inverse Problem in Determining the Normal and Tangential Drag Coefficients of Marine Cables

The Levenberg-Marquardt method is applied to estimate simultaneously the normal and tangential drag coefficients of marine cable, in a planarly towed cable-body system, from the measurements of the horizontal and vertical tension force components. Because only coefficients are to be estimated, this type of problem belongs to a branch of systems identification called "parameters estimation" (Beck & Blackwell 1988). A statistical analysis is performed to determine the standard deviation and the approximate confidence bounds for estimating the normal and tangential drag coefficients. Results show that the sensitivity and accuracy of the estimated coefficients depend on the type of boundary conditions used in the direct problem as well as on the towed configurations.

Dynamic analysis of three-dimensional marine cables

Marine cables are widely used in a variety of offshore activities. In this paper, a numerical approach is presented which is capable of predicting the dynamic behaviour of three-dimensional marine cables. The solution of this problem is of practical importance in the estimation of dybamic loading and motion, and thus has direct application to the enhancement of safety and the effectiveness of the offshore activities. The approach is based upon the lump-mass-and-spring model and the finite difference method. Mathematical analysis is provided on the basic characteristics of the model and the numerical stability. A numerical example is given to demonstrate the validity of the approach.

Static Analysis of Marine Cables via Shooting‐Optimization Technique

Previous studies by De Zoysa and Chucheepsakul on a three-dimensional static analysis of marine cables yielded contradictory results for an example problem. This work addresses this discrepancy and furnishes the correct expressions for the set of differential equations governing the cable problem. The so-called shooting-optimization method is proposed as a solution technique. De Zoysa’s cable problem was resolved, and presented herein are the correct variations of the tension components at the bottom end of the cable with respect to different angles between the ocean current direction and the projection of the ship-to-buggy line onto the horizontal plane.

A semi-analytic treatment of three-dimensional statics of marine cables

A semi-analytic approach is presented in this paper which is capable of predicting the static performance of marine cables. The solution is derived as a function of only three parameters which can be solved numerically by implementing different kinds of boundary conditions. The efficiency and accuracy of the method permit quick parametric studies for optimal selection of the system particulars which is undoubtedly useful for preliminary design. A number of numerical examples demonstrates the validity of the approach adopted.

A numerical method for predicting snap loading of marine cables

A numerical approach for predicting the snap loading of marine cables operating in alternating taut-slack conditions is presented. The modelling is based upon the lumped-mass-and-spring method with modifications to take into account the bilinear axial stiffness of the cable. The resulting governing equations are integrated in the time domain using the modified Euler method. Numerical examples are given and comparisons of the numerical results and the experimental results available are made which demonstrate the validity of the present method.

The Influence of the Shear-Wave Structure of the Sea Bed on the Seismic Wavefield

Much modelling of the seismic wave field is undertaken with an acoustic approximation in which the influence of shear waves is neglected. Although such calculations can predict the correct travel times for compressional (P) wave propagation, they can be very misleading with respect to the distribution of seismic amplitudes, especially at larger offsets. At the sea bed, the acoustic approximation predicts total reflection for P waves incident beyond the critical angle. However, once the presence of shear waves in the solid material of the sea floor is taken into account, P waves in the water can give rise to transmitted S waves with a major change in the propagation pattern. The effects are very important for hard sea bottoms such as those on the Northwest Shelf. The character of the water-borne noise in these conditions depends on whether the shear-wave speed at the sea bed lies above or below the P-wave velocity in the sea water above. For high shear velocities, two distinct sets of critically reflected multiples can be produced to give a very energetic noise train trapped in the water column. Conversion of P to S in transmission at the sea floor can often be important and give rise to significant arrivals on the outer traces from long marine cables. Synthetic seismogram calculations for large offsets, with selective control of the level of multiples and conversion at each interface, provide a convenient tool for characterizing the expected water-borne energy and the influence of converted shear waves on the pressure field recorded in the water.

On the axial-torsional structural behaviour of flexible pipes, umbilicals and marine cables

An analytical model for predicting the axial-torsional structural behaviour of flexible pipes, umbilicals and marine cables is presented. The analytical model is based on the interaction between the component layers of a generic flexible structure. The flexible structure is analysed as a combination of helical and cylindrical components placed in arbitrary order. A governing equation for the flexible structure is derived, the solution of which provides the axial-torsional load-displacement relationship. The model also provides additional information, such as the construction of individual component layers, interfacial contact pressures and interlayer gap amplitudes. Results are presented for a typical marine cable, an umbilical and a flexible pipe. Tensile tests have been carried out on the marine cable and the umbilical and good agreement between theory and experiment is demonstrated.

On the flexural structural behaviour of flexible pipes, umbilicals and marine cables

A general analytical model to predict the flexural structural behaviour of multiple layer flexible structures such as flexible pipes, umbilicals and amrine cables is presented. The flexural response of these structures is shown to be dominated by relative movement between component layers once a critical curvature has been exceeded. This slip mechanism leads to a hysteretic bending moment-curvature relationship for generic flexible structures. Bending tests have been carried out on three representative specimens consisting of a marine cable, an umbilical and a flexible pipe. Satisfactory agreement between theory and experiment is demonstrated.

Efficient Static Analysis and Design of Flexible Risers

An improved cable element for static analysis is presented based on the equations of an elastic catenary. The element includes an algorithm for adaptive discretization when fluid drag forces are present. Hence, a single element can be used to model many marine cables, regardless of length. The element is applied to flexible riser analysis and preliminary design, which is automated by solving a nonlinear programming problem. Results demonstrate that a practical automated design method can be developed following the procedure presented here.

Dynamic response of viscoelastic cable elements

A finite element model of the dynamic viscoelastic response of marine cables was developed using an updated Lagrangian description of the principle of virtual work and a three-parameter linear viscoelastic constitutive equation for synthetic cables. This model can be used for dynamic analysis of complexly connected and curved systems of cables in the ocean. Two simple examples were considered: a point load on a changing cable which gave comparisons of two different numerical solution methods to an exact solution, and the periodic response to an initial transverse disturbance of a straight segment, which was used to demonstrate and validate the finite element model.

Vortex-Induced Strumming Vibrations of Marine Cables With Attached Masses

Twenty full-scale test runs were conducted during the cable strumming experiments reported in this paper. These consisted of ten pairs of equivalent tests conducted in air and in water with a cable fitted with arrays of attached masses. The measured in-air natural frequencies are in good agreement with computed code predictions for the second and higher (up to n = 5) cable modes. The first mode frequency apparently was influenced by the sag of the cable. The measured mode shapes of the cable vibrations in water also are in agreement with the computed mode shapes. For the experiments in water the computed and measured natural frequencies are in good agreement. Drag coefficients in the range CD = 2.4 to 3.2 were commonly observed when the cable-attached mass system was strumming due to the water flow past it.

Vortex-excited vibrations of marine cables : O. M. Griffin et al. Proc. ASCE, J. Waterway Port Coast. Ocean Div. May 1980, 106(WW2), 183–204

Abstract : A field study of the vortex-induced oscillations of 76.5 ft lengths of various marine cables was conducted. The test site, a sandbar at the mouth of Holbrook Cove in Castine, Maine, was chosen to insure uniformity of current over the entire test length. The flow of the incoming tide produced transverse vibrations of the test cable over a broad range of Reynolds of numbers. Cable tension could be varied as desired. The amplitude, frequency, and general behavior of the cable motions were recorded. The results have been compared to the findings of previous investigators, and interpreted in the light of known properties of the body-wake interaction. A method of testing anti-strumming fairings is also presented, along with the results of such a test. (Author)

Free Vibrations of Taut and Slack Marine Cables

The natural frequency and damping of several typical marine cables were measured in air and in water and are reported in this paper. The changes in natural frequency and mode shape that occur in both media as the cable sags from a taut configuration are in agreement with a recently developed linear theory. A modal crossover predicted by the theory was also observed as the cable tension was decreased. The onset of the catenary behavior has been identified and it coincides with at least an order of magnitude increase in the structural damping of the cables. The fluid dynamic contributions to the virtual mass and the damping are found to be independent of the sag in the cable and are comparable to measurements for taut cables reported in the literature.

Historical Background of Vinyl Foams

Abstract The development of vinyl foam technology goes back to the early 1940s when vinyl resins began to emerge as an important new synthetic polymer. In 1941 Wick and Grassl [1] of I. G. Farben-Bitterfeld disclosed the availability of foamable PVC pastes based on Igelit PCU. Subsequently, I. G. Farben developed a high-pressure molding process for both rigid and flexible PVC using organic blowing agents such as Porofor N (AZDN) and Porofor PB (DAB) [2]. Between 1941 and 1945 Continental Rubber Works, Hanover and Dynamit A.G., Troisdorf, Germany, produced substantial quantities of expanded PVC by this method. The cellular PVC was fabricated into unsinkable rafts, fire-and oil-resistant insulation, and floats for fishing nets and marine cables [2, 3]. In England, Expanded Rubber Co. was in full production of expanded PVC pads for the aircraft industry in 1945 [4], while in the United States, Sponge Rubber Products, Shelton, Connecticut, U.S. Rubber, Mishawaka, Indiana, and Great American Industries, Bedfor...

Corrosive Action of Sulfur against Metallic Copper during Vulcanization

Abstract The use of copper wire electroplated with tin for insulated electric wires was originated by Siemens eighty-five years ago (through Saito, J. Soc. Chem. Ind. Japan, 18, 248 (1915)), and its merits lie in the fact that it prevents a lowering of the electrical conductivity and mechanical strength from corrosion of copper by the sulfur in the rubber, and also prevents the rubber from deteriorating abnormally fast by contact with the copper. The manufacture of rubber for coating wire has improved rapidly since the appearance of organic accelerators and combined accelerating and vulcanizing agents, such as the polynitrobenzenes and benzoyl peroxide of Ostromislensky, the selenium of Boggs and tetramethylthiuram tetrasulfide and tetramethylthiuram disulfide. Recently, it was reported (India Rubber World, 87, 38 (1933)) that rubber compounded with 2 per cent of 1,3,5-trinitrobenzene as vulcanizer does not corrode wire conductors and does not deteriorate abnormally fast when the rubber mixture is covered directly on the wire and vulcanized. The prediction was also made that tin-coated copper wire will disappear entirely from the cable world. As a matter of fact, marine cables have for a long time been covered with an insulator consisting chiefly of gutta-percha or balata hydrocarbon, in direct contact with the copper conductor, and have given good service. The para-gutta insulation of marine cables, recently developed by the Western Electric Company, U. S. A., is composed partly of rubber, with no tin coating on the copper conductor. Nevertheless, the principal factor which decides the “electrical life” of rubber submerged in water is, according to Curtis (J. Res. Natl. Bur. Standards, 5, 539 (1930)) the deterioration of the rubber by copper salts, and Asano (J. Soc. Chem. Ind. Japan, 24, 336 (1921)) reported that smoked sheet became so sticky that it required considerable strength to separate after it had been held between two copper plates for six months. The status of the electric insulating wire industry today is such that a thorough investigation of the tin coating of copper wire and the methods of tin coating in connection with the deterioration of rubber by the copper wire is desirable. The investigation described in the present paper was carried on with this object, and it deals with experiments on the corrosion of metallic copper by sulfur during vulcanization, and shows the formation of copper sulfides as corrosion products.

Constitutional Law. War Powers. Taking over of Marine Cables after Armistice

Constitutional Law. War Powers. Taking over of Marine Cables after Armistice

On the failure to lay the submarine cable

This paper presents the formulation and solution of governing equations that can be used to analyse the three-dimensional (3D) behaviour of either marine cables during installation or the response of segmented elastic mooring line catenaries as used for floating offshore structures when both are subjected to arbitrary sheared currents. The methodology used is an extension of one recently developed for analyses of marine cables when being installed on the seabed or being towed. The formulation describes elastic cable geometry in terms of two angles, elevation and azimuth, which are related to Cartesian co-ordinates by geometric compatibility relations. These relations are combined with the cable equilibrium equations to obtain a system of non-linear differential equations, which are numerically integrated by fourth and fifth order Runga–Kutta methods. The inclusion of cable elasticity and the ability to consider arbitrary stored currents are key features of this analysis. Results for cable tension, angles, geometry and elongation are presented for three example cases—the installation of a fibre optic marine cable, the static analysis of a deep water mooring line and the response of a telecommunications cable to a multi-directional current profile.