Dynamic Analysis of Towed and Variable Length Cable Systems

Towed cable systems are frequently used in marine measurements where the length of the towed cable varies during launch and recovery. In this paper a novel method for modeling variable length cable systems is introduced based on the finite segment formulation. The variable length of the towed cable is described by changing the length of the segment near the towing point and by increasing or decreasing the number of the discrete segments of the cable. In this way, the elastic effects of the cable can be easily handled since geometry and material properties of each segment are kept constant. Experimental results show that the dynamic behavior of the towed cable is consistent between the model and the physical cable. Results show that the model provides numerical efficiency and simulation accuracy for the variable length towed system.

A new cable truss support system for coal roadways affected by dynamic pressure

The support of coal roadways is seriously affected by intense dynamic pressures.This can lead to problems with large deformation of the roof and the two side walls of coal roadways.Rapid convergence of the walls and roof,a high damage rate to the bolts and cables,or even abrupt roof collapse or rib spalling can occur during the service period of these coal roadways.Analyzing the main support measures used in China leads to a proposed new cable truss supporting system.Thorough study of the entire structure shows the superiority of this design for roadways suffering under dynamic pressure.A corresponding mechanical model of the rock surrounding the cable truss system is described in this paper and formulas for calculating pre-tightening forces of the truss cable,and the minimum anchoring forces,were deduced.The new support system was applied to a typical roadway affected by intensive dynamic pressure that is located in the Xinyuan Coal Mine.The results show that the largest subsidence of the roof was 97 mm,the convergence of the two sides was less than 248 mm,and the average depth of the loose,fractured layer was only 6.12 mm.This proves that the new support system is feasible and effective.

Dynamics analysis of planar armored cable motion in deep-sea ROV system

The armored cable used in a deep-sea remotely operated vehicle(ROV) may undergo large displacement motion when subjected to dynamic actions of ship heave motion and ocean current. A novel geometrically exact finite element model for two-dimensional dynamic analysis of armored cable is presented. This model accounts for the geometric nonlinearities of large displacement of the armored cable, and effects of axial load and bending stiffness. The governing equations are derived by consistent linearization and finite element discretization of the total weak form of the armored cable system, and solved by the Newmark time integration method. To make the solution procedure avoid falling into the local extreme points, a simple adaptive stepping strategy is proposed. The presented model is validated via actual measured data. Results for dynamic configurations, motion and tension of both ends of the armored cable, and resonance-zone are presented for two numerical cases, including the dynamic analysis under the case of only ship heave motion and the case of joint action of ship heave motion and ocean current. The dynamics analysis can provide important reference for the design or product selection of the armored cable in a deep-sea ROV system so as to improve the safety of its marine operation under the sea state of 4 or above.

Numerical Modeling of a Spherical Buoy Moored by a Cable in Three Dimensions

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code Proteus DS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.

A Geometrically Exact Formulation for Three-Dimensional Numerical Simulation of the Umbilical Cable in A Deep-Sea ROV System

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle（ROV） system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized-a implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

Numerical simulation of deepwater deployment for offshore structures with deploying cables

Deepwater deployment of offshore structures in different sea states was investigated. The whole deployment system was modeled as a lumped mass model, and discretization scheme for cable geometry and methodology for calculating the internal and external force acting on deploying cable were presented. The deployment model suitable for the time-varying length of deploying cable was specified. The free-surface flow fields together with the ship motions were used to calculate dynamic tension in the deploying cable during deployment of the structure. The deployment of deep sea mining system which was a typical subsea working system was employed. Based on lumped mass analysis model and parameters of deep sea mining system, numerical simulations were performed, and dynamic load and dynamic amplification factor(DAF) with different cable parameters, deploying velocities and sea states were obtained. It is shown that cable parameters and amplitudes of ocean waves can significantly influence the dynamic load and DAF, and the time-varying natural period of deploying system is a dominant factor, while the effect of deploying velocity is not obvious.

Transient Dynamic Analysis of A Variable-Length Rope-Driven Wave Energy System

A new dynamic model of a variable-length rope,which could be used for the transient analysis of a buoy-rope-generator(BRG)wave energy system,was proposed in this paper.The model started from the basic dynamic equations of variable mass system,and took into account the physical properties such as axial force,shear and bending.According to the principle of D'Alembert-Lagrange,the equivalent integral weak formulation was firstly obtained,and through consistent linearization and isoparametric discretization,the finite element model of the variable-length rope was then derived.The Bathe scheme was employed to solve the model numerically,based on its excellent performance in solving nonlinear dynamic problems,and an automatic time step size algorithm was designed according to the number of iterations of the two substeps of Bathe scheme.The procedures of rope mesh regeneration were also put forward,where only one variable-length element was always located at the top end of the rope,and the rest were all fixed-length elements.The proposed variable-length rope model and solution schemes were verified through comparison with the results of a tank experiment.Finally,the transient dynamics of a kind of BRG system was analyzed and discussed.

Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.

NUMERICAL INVESTIGATION OF SEABED INTERACTION IN TIME DOMAIN ANALYSIS OF MOORING CABLES

In this paper, an efficient two-dimensional finite element model for numerical analysis of mooring cables and seabed interaction has been built. Geometric shape and dynamics of mooring cables are computed in time domain, accounting for the motions of the moored sturcture. In the model, a hybrid beam element is employed to simulate the mooring cable while the seabed is simulated by application of different soil constitutive models. After the elastic and elastic-plastic soil constitutive models have been used for computation, tensions and offsets of mooring cables at fairlead point are also compared accounting for friction effect between cables and seabed. Both transversal and longitudinal behaviors are studied at different water depths.