Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method

This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler’s equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.     

Numerical Prediction of Vortex Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration （VIV） of top tensioned riser （Till）, the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti＇ s wake oscillator model. Then Galerkin＇ s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and file corresponding numerical programs are compiled which solve the coupled equations directly in the time domain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7 is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers. The effect of internal flow on the dynamic characteristics and dynmnic response of the riser is analyzed and several valuable conelusions are drawn.     

Numerical Prediction of Vortex-Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration (VIV) of top tensioned riser (TTR), the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti''s wake oscillator model.Then Galerkin''s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and the corresponding numerical programs are compiled which solve the coupled equations directly in the timedomain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers.The effect of internal flow on the dynamic characteristics and dynamic response of the riser is analyzed and severalvaluable conclusions are drawn.     

Experimental study and numerical simulation on vortex-induced vibration of flexible riser

In order to study the effect of internal flow on vortex-induced vibration of flexible riser, the experiment on the vortex-induced vibration of flexible riser transporting fluid in the current was conducted in the physical oceanography laboratory of Ocean University of China. Considering the internal flowing fluid and external marine environment, the dynamic response of the flexible riser was measured. The corresponding numerical simulation was performed using the wake oscillatory model considering the extensibility of the riser system. Both the experiment and the numerical simulation indicated that with the increase of internal flow speed, the response amplitude increases, while the response frequency decreases.     

Numerical and Physical Investigation on Vortex-Induced Vibrations of Marine Risers

1 .Introduction Risers ,in deep water and strong current environments ,are prone to vortex-induced vibrations(VIV) .Vortex-inducedforces may excite the risersintheir normal modes of transverse direction.Un-der the“lock-in”condition,large resonant oscill…     

考虑温度应力下深海输油立管动力特性及响应研究

考虑深海输油立管管内外温差产生的温度应力以及管内流体流动和管外海洋环境荷载的共同作用,建立了深海输油立管振动微分方程,采用有限元法对输油立管动力特性及动力响应进行求解,并将考虑温度应力及不考虑温度应力的立管动力特性及在波浪作用下的立管动力响应进行了对比。结果表明,对于动力特性,温度应力的存在会使得立管自振频率降低;对于动力响应,会使得波浪作用下动力响应幅值增强而频率略有降低,易引起立管的疲劳破坏。     

A vortex induced vibration of marine riser in waves

A marine riser transporting fluid in the Bohai Sea was selected as study object,using an experi-mental and numerical method to study its vortex induced vibration in waves. A similarity theory was used in the experiment to derive the experimental model from a practical model,the dy-namic response of a riser model was measured in waves. A corresponding numerical simulation was performed using a finite element method. Comparisons were made with the results between the experiment and the numerical simulation. Some valuable results were obtained.     

An updated Lagrangian finite element formulation for large displacement dynamic analysis of three-dimensional flexible riser structures

An updated Lagrangian finite element formulation of a three-dimensional annular section beam element is presented for large displacement and large rotation dynamic analyses of flexible riser structures. In this formulation a new linearization method is used to avoid inaccuracies normally associated with other linearization schemes. The effects of buoyancy force as well as steady state current loading are considered in the finite element solution for riser structures response. The formulation has been implemented in a nonlinear finite element code and the results are compared with those obtained from other schemes reported in the literature.     

Nonlinear dynamics of an elastic cable during laying operations in rough sea

A numerical approach for predicting motion and tension of extensible marine cables during laying operations in a rough sea is presented here. The solution methodology consists of dividing the cable into straight elements, which must satisfy an equilibrium equation and compatibility relations. The system of nonlinear differential equations is solved by the Runge–Kutta method, taking the effect of regular and/or irregular waves into account explicitly.

Illustrative applications of the method are given for a typical cable laying ship. The results are presented as rms values of the cable dynamic tension and corresponding dynamic factor for two different types of cable and several values of cable stiffness. The effect of axial deformation on the maximum tension at the shipboard pulley location is highlighted.     

Dynamic response of marine risers by single wave and spectral analysis methods

This paper uses the Galerkin method in the solution of the marine riser differential equation and compares the dynamic bending stresses in a tension-leg-platform riser calculated by the linearised single wave and linearised spectral analysis methods.The results show that it is possible to make some rational assessment of approximate peak values of bending stress in the spectral method.The analysis methods are applicable to any riser system subject to horizontal exciting forces due to fluid and vessel motion.     

多频参激—涡激联合作用下顶张力立管分岔分析

复杂海洋环境中,顶张力立管顶部平台受到不同分量叠加的波浪作用,导致其轴向张力与多个频率相关,系统产生多频参激与涡激的联合振动,其动力学行为变得更为复杂,尤其是分岔和混沌等非线性振动特性有待进一步分析。首先,基于欧拉—伯努利梁理论,引入范德波尔尾流振子,建立和推导受多频参激—涡激联合作用下立管的动力学模型及其运动微分方程;接着,利用伽辽金法得到离散后的常微分方程组,采用多尺度法得到系统共振响应的调谐方程;最后,通过数值算例探究系统在多源和多频载荷联合作用下的共振响应。结果表明：对于多频参数激励,其中一个参数激励幅值在立管振动中起主导作用,而另一个会引起分岔的位置、数量和性质发生改变;随质量—阻尼参数增大,系统共振响应幅值整体先增大后减小,各分岔点出现的位置整体先向泄涡频率较大处移动,随后向泄涡频率较小处移动;质量—阻尼参数的变化还可能诱使系统发生倍周期分岔和混沌现象,危害结构安全。此外,采用直接数值积分求解微分方程组,验证近似分析结果,两者吻合较好。     

Three-dimensional Lump-Mass formulation of a catenary riser with bending, torsion and irregular seabed interaction effect

A three-dimensional Lump-Mass formulation of a catenary riser, capable of handling irregular seabed interaction, with bending and torsional stiffness is presented in this paper. This formulation uses only three degrees of translational freedom and one independent torque variable for each computational node. The generality of the present formulation permits static and dynamic analyses of a wide range of offshore-related slender structure systems such as mooring cables, rigid and flexible risers as well as submarine pipelines. Four sets of results are presented for (i) a hanging catenary, (ii) as (i) but subjected to end torsion, (iii) a wire, chain and spring buoy mooring and (iv) a steel catenary riser on an irregular seabed.     

顶部浮体激励下钢悬链线立管的动力响应分析

考虑钢悬链线立管大变形的特性以及内流的影响,利用Kane方法和拉格朗日应变理论建立钢悬链线立管的二维动力学模型。将顶部浮体的激励简化为一个沿顺流向的周期作用力施加于立管顶部,采用平均加速度法求解立管的动力响应。探讨顶部浮体不同激励频率下立管的非线性动力响应以及内流流速的大小对管道共振响应幅值的影响。     

Dynamic and static analysis of a marine riser

A frequency domain normal mode solution is presented for the dynamic response of an unbuoyed marine riser subjected to periodic excitation from a surface vessel in the direction of wave propagation. The variable tension beam-column equation is solved in terms of normal modes of free vibration of the riser and the rigid body displacement. Drag forces on the riser are represented by Morison's formula taking account of the velocity of the riser and wave-induced fluid velocity. A periodic solution for the flexural motion of the riser and the bending stress is then obtained by means of an iterative solution of the frequency response function. The drag force induced stresses arising from a linearly varying current are also determined. The results presented compare favourably with those obtained by other methods.     

Behavior of unbonded flexible risers subject to axial tension

Owing to nonlinear contact problems with slip and friction, a lot of limiting assumptions are made when developing analytical models to simulate the behavior of an unbonded flexible riser. Meanwhile, in order to avoid convergence problems and excessive calculating time associated with running the detailed finite element （FE） model of an unbonded flexible riser, interlocked carcass and zeta layers with complicated cross section shapes are replaced by simple geometrical shapes （e.g. hollow cylindrical shell） with equivalent orthotropic materials. But the simplified model does not imply the stresses equivalence of these two layers. To solve these problems, based on ABAQUS/Explicit, a numerical method that is suitable for the detailed FE model is proposed. In consideration of interaction among all component layers, the axial stiffness of an eight-layer unbonded flexible riser subjected to axial tension is predicted. Compared with analytical and experimental results, it is shown that the proposed numerical method not only has high accuracy but also can substantially reduce the calculating time. In addition, the impact of the lay angle of helical tendons on axial stiffness is discussed.     

Large deformation three-dimensional static analysis of deep water marine risers

The problem of static three-dimensional, nonlinear, large deformation response of a marine riser is formulated within small strain theory and solved numerically. This type of analysis is necessary, for the new generation of drilling and production risers. The mathematical model takes properly into account the effects of internal and external pressure and the complete nonlinear boundary conditions, without linearizing the follower forces. The extensibility or inextensibility condition is used as the constitutive relation in the tangential direction. Torsion and bending are coupled. The external load and the boundary conditions are deformation dependent. A solution method is developed based on an incremental finite element algorithm, which involves a prediction-correction scheme. In the correction phase deformation dependent quantities are updated. The extensibility or inextensibility condition is used to reduce the degrees of freedom of the system. The numerical results of the developed computer code compare very well with available semi-analytical and numerical solutions. Three numerical applications are used to demonstrate the importance of large deformation, nonlinear and three-dimensional analyses.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

The effect of nonlinear multi-contact coupling with gap between risers and guide frames on global spar motion analysis

Nonlinear multi-contact coupling between vertical risers and guide frames inside the spar moon-pool is studied. The existing numerical model for hull/mooring/riser coupled dynamics analysis treats riser as an elastic rod truncated at the keel (truncated riser model), and the risers are free to slide in vertical direction with constant tension, while restricted in horizontal direction. The truncated riser model neglects the portion of the riser inside the moon-pool and tends to overestimate the spar pitch motion. In the newly developed model, the risers are extended through the moon-pool with realistic boundary conditions at multiple guide frames, and thus additional contact forces and moments on the spar hull are considered. The gap effects between the riser buoyancy-cans and riser guide frames are also modeled using three different types of gap springs. Their different dynamic characteristics are extensively studied. The new riser model also considers the Coulomb damping between buoyancy-cans and riser guide frames and also allows the impact-like contact force calculation on risers for ensuring fatigue analysis.     

A finite difference approximation for dynamic calculation of vertical free hanging slender risers in re-entry application

The dynamic calculations of slender marine risers, such as Finite Element Method (FEM) or Modal Expansion Solution Method (MESM), are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation (FDA) method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bernoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser’s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.