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.

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 Modeling of a Spar Platform Tethered by a Mooring Cable

Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, Proteus DS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.

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.