Bounded and unbounded coupled transverse response of parametrically excited vertical marine risers and tensioned cable legs for marine applications

The paper deals with the non-linear dynamic response in the transverse direction of vertical marine risers or a tensioned cable legs subjected to parametric excitation at the top of the structure. The dynamic model contains both elastic and bending effects. The analytical approach reveals that the dynamic lateral response is governed by effects originated from the coupling of modes in transverse direction. The mathematical model is being treated numerically by retaining a sufficient number of transverse modes. Numerical results are given for specific case studies and refer both to the time histories of the lateral response for all modes of motion, and to the corresponding power spectral densities obtained through FFT. The numerical predictions are suitably plotted and discussed. The calculations concern both the undamped and the damped dynamic system. The damping in the system is a non-linear Morison type term, which describes the effect of the hydrodynamic drag. Both coupled and uncoupled equations are treated and points as well as regions of coupled and uncoupled stability and instability are defined. It is shown that the impacts originated from the coupling, evaluate new instabilities for the respective undamped system. The numerical results obtained through FFT of the time histories, provide qualitative conclusions for the features of the dynamic response for the modes of motions considered. Special attention has been paid to the effect of the hydrodynamic drag for the parametric excitation frequencies that guide the dynamic system to lie within a region of coupled instability.     

A finite differences formulation for the linear and nonlinear dynamics of 2D catenary risers

A finite differences (FD) solution method is proposed for the numerical treatment of the dynamic equilibrium problem of 2D catenary risers. The method is based on the so-called Box approximation, which in the scope of the present contribution is applied to the complete nonlinear model as well as to the reduced linearized formulation. The application of the Box method transforms the original governing systems into convenient sets of algebraic equations, which in turn are solved efficiently by the relaxation method. Extensive numerical calculations are presented that describe the dynamic behaviour of the structure and evaluate the amplification in loading due to the dynamic components. The effect of the geometric nonlinearities is assessed through comparative calculations that concern both mathematical formulations examined in the present, i.e. the complete nonlinear, and the reduced linearized model. Special attention is paid to the heave excitations as they amplify significantly the magnitudes of the loading components.     

A finite element method for dynamic analysis of long slender marine structures under combined parametric and forcing excitations

This paper presents a numerical analysis of lateral responses of a long slender marine structure under combined parametric and forcing excitations. In the development of the 3-D numerical program, a finite element method is implemented in the time domain using the Newmark constant acceleration method. Some example studies are performed for various water depths, environmental conditions and vessel motions. The relative amplitudes of combined excitations to a conventional forcing excitation are examined. The response amplitude of a combined excitation is much greater than that of a forcing excitation in the even number of instability regions of the Mathieu stability chart. The results demonstrate that a combined excitation needs to be considered for the accurate dynamic analysis of long slender marine structures subjected to a surface vessel motion.     

Non-Linear Response of Tethers Subjected to Parametric Excitation in Submerged Floating Tunnels

For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels,a theoretical model for coupled tube-tether vibration is developed.Upon the assumption that the static equilibrium position of the tether is a quadratic parabola,the governing differential equations of the tether motion are derived by use of the Hamilton principle.An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method.The results show that,when the static equilibrimn position of the tether is assumed to be a quadratic parabola,the tether sag effect on its vibration may be reflected;the tether sag results in the asymmetry of tether vibration amplitude;for the reduction of the tether amplitude,the buoyant unit weight of the tether should approach to zero as far as possible during the design.     

Analysis of roll motion and stability of a fishing vessel in head seas

The present paper describes an investigation on the relevance of parametric resonance for a typical fishing vessel in head seas. Results for different Froude numbers are discussed based on experimental, numerical and analytical studies.The first region of resonance is investigated. Distinct wave amplitudes are considered. Some intense resonances are found to occur. The paper compares the experimental results with non-linear time simulations of the roll motion. Very good agreement is found, even when large motions take place.Finally, in order to analyze the experimental/numerical results, analytic consideration is given to distinct parameters affecting the dynamic process of roll amplification. The influence of heave, pitch, wave passage effect, speed and roll restoring characteristics are discussed.     

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。     

A study on the Local Joint Flexibility (LJF) of two-planar tubular DK-joints in jacket structures under in-plane bending loads

In the present paper, results of a parametric study conducted on the Local Joint Flexibility (LJF) of two-planar tubular DK-joints under In-Plane Bending (IPB) loads are presented. DK-joints are among the most common joint types in jacket substructure of Offshore Wind Turbines (OWTs). A total of 324 finite element (FE) analyses were carried out on 81 FE models under four types of IPB loading in order to investigate the effect of the DK-joint’s geometrical parameters on the LJF factor (f_LJF). Based on the results of parametric study, the factors leading to the LJF reduction were introduced. Generated FE models were verified using the existing experimental data, FE results, and parametric equations. The effect of the weld profile was also considered. The f_LJF in two-planar DK- and uniplanar K-joints were compared. Results indicated that the effect of multi-planarity on the LJF is quite significant and consequently the use of the equations already available for uniplanar K-joints to calculate the f_LJF in two-planar DK-joints may lead to highly under-/over-predicting results. To handle this issue, the FE results were used to derive a set of parametric equations for the prediction of the f_LJF in IPB-loaded two-planar DK-joints. The proposed equations were checked against the acceptance criteria recommended by the UK DoE and can be reliably used for the analysis and design of tubular joints in OWTs.     

考虑土骨架加速度效应的海床动力反应及其影响因素分析

由Biot二维广义动力固结理论的形式基本控制方程出发,忽略孔隙流体的加速度,提出了饱和海床动力反应的时域有限元数值解法.联立静力平衡条件和Biot固结方程的退化法所得到的数值解可视为其特例.在比较算例中,退化法得到的超静孔压和有效应力幅值沿海床深度的分布与解析解一致.一般情况下,土骨架的加速度对海床的有效应力和超静孔压影响很小,控制方程可以退化为Biot理论.成层海床上部的粗砂层不会使超静孔压幅值在海床表面下较浅的深度内迅速衰减,难以改变海床的瞬时循环液化深度.     

Effects of ship motion on a neutrally-stable towed fish

Digital computer simulation in two dimensions of a neutrally-stable fish towed on a faired cable has been used to investigate the response of the fish to disturbances in the ship motion. The numerical methods used are described broadly, excluding mathematical detail, and selected results are presented which indicate typical behaviour of the system.The free oscillations of the fish-cable system and its response to deterministic and random ship disturbances are investigated. This reveals the dynamic principles governing the motion and allows the formulation of simple rules to give a first approximation to the magnitude of the fish response. It is shown that, provided resonances of the ship and fish-cable system do not coincide, the overall amplitude of motion of the fish is proportional to the sine of the angle made by the top of the cable with the horizontal. Formulae are given for calculating approximately the resonant frequencies of the towed system.     

PSME model of parametric excitation of two-layer liquid in a tank

Internal waves driven by external excitation constitute important phenomena that are often encountered in environmental fluid mechanics. In this study, a pseudospectral σ-transformation model is used to simulate parametric excitation of stratified liquid in a two-layer rectangular tank. The σ-transformation maps the physical domain including the liquid free surface, the interface between the liquid layers, and the bed, onto a pair of fixed rectangular computational domains corresponding to the two layers. The governing equation and boundary conditions are discretised using Chebyshev collocation formulae. The numerical model is verified for two analytical sloshing problems: horizontal excitation of constant density liquid in a rectangular tank, and vertical excitation of stratified liquid in a rectangular tank. A detailed analysis is provided of liquid motions in a shallow water tank due to excitations in the horizontal and the vertical directions. Also, the effect of pycnocline on the wave motions and patterns is studied. It is found that wave regimes and patterns are considerably influenced by the pycnocline, especially when the excitation frequency is large. The present study demonstrates that a pseudospectral σ-transformation is capable to model non-linear sloshing waves in a two-layer rectangular tank.     

Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

Numerical modelling of liquefaction in loose sand deposits subjected to ocean waves

The failure of marine structures is often attributed to liquefaction in loose sand deposits that are subjected to ocean waves. In this study, a two-dimensional integrated numerical model is developed to characterize the liquefaction behaviours of loosely deposited seabed foundations under various types of ocean waves. In the present model, Reynolds-Averaged Navier–Stokes (RANS) equations are used to simulate the surface wave motion, and Biot's consolidation equations are used to link the solid-pore fluid interactions in a porous medium. A poro-elasto-plastic solution is used to reproduce foundation behaviour under cyclic shearing. Unlike previous investigations, both oscillatory and residual soil responses were considered; they are coupled in an instantaneous approach. Verification of the model results to the previous centrifugal wave tests is carried out, obtaining fairly good agreement. Numerical examples show that foundation behaviour under various types of wave loading, particularly standing waves or a solitary wave, embodies a completely two-dimensional process in terms of residual pore pressure development. The parametric studies demonstrate that liquefaction caused by the build-up of pore pressures is more likely to occur in loosely deposited sand foundations with poor drainage and under large waves.     

Numerical analysis on random wave-induced porous seabed response

Research on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.     

波浪与多孔介质结构相互作用SPH模拟

应用经CSPM法和黎曼解修正后的光滑粒子流体动力学(SPH)方法,建立了主动吸收无反射数值波浪水槽,研究波浪作用下多孔介质结构的水动力特性。流体运动控制方程采用N-S方程,多孔渗水结构内流体的运动控制方程考虑渗流力的影响。数值计算结果给出了水槽内不同位置测点的波面历时曲线和越浪量随时间变化曲线,并同试验结果和Philip Liu的数值计算结果进行了比较。并对一个波浪周期内斜坡堤多孔介质结构内外的速度场和压力分布进行了讨论分析。计算分析表明,数值计算波面较Philip Liu的计算结果与试验结果吻合更好。说明应用SPH方法建立的二维数学模型能够较好地模拟破碎波在多孔渗水斜坡上的爬坡和越浪。     

随机波作用下海床动态响应分析

真实的海洋波浪是随机的,而前人对海床的动态响应分析大都是选用线性波或者Stokes波理论,对海床的模拟大都采用Biot拟静力模型,忽略了流体速度及土体位移加速度的影响。联合使用Longuet-Higgins随机波模型(采用Jonswap谱)以及动力u-p形式的海床响应计算模型,使用COMSOL Multiphysics多场耦合软件的PDE模块输入方程进行有限元计算,得到随机波作用下整体海床动态响应结果。将随机波结果与一阶Stokes波和椭圆余弦波结果进行对比,并对渗透系数和饱和度进行参数分析,研究表明渗透系数和饱和度对于随机波作用下海床动态响应影响显著。     

Dynamic Behavior of Beam–Pile Structure Under Vertical Transient Excitation

The dynamic response of beam–pile–soil system under vertical transient excitation is investigated. Both piles and beam are assumed to be one-dimensional rods and subjected to vertical exciting forces. The uniformly distributed Voigt models are introduced to simulate the pile tip resistances, and the dynamic interactions between piles and beam are simplified as a set of concentrated point loads. Then, the plane strain model, the theory of longitudinal vibration of one-dimensional rod, and the Timoshenko beam theory are used to establish the mathematical models for the motion of soil, piles, and beam, respectively. On this basis, the matrix equation for solving the governing equations is constructed in the Laplace domain and the time-domain response is then obtained by the discrete inverse Fourier transform. Comparisons with numerical simulations and model tests are conducted to evaluate the rationality of the present solution. The results show that the dynamic responses calculated by the proposed solution are generally consistent with simulated curves and experimental data.     

Influence of viscosity on one-dimensional thermal consolidation of marine clay

ABSTRACT

The elastic mechanical response of porous materials under a heat source has many applications in civil engineering and has received considerable attention in the geotechnical literature. In this paper, a Kelvin viscoelastic model is combined with the thermohydromechanical governing equations for marine clay and solved using a numerical inversion of the inverse Laplace transform in the time domain. After validation against existing analytical solutions, numerical parametric studies are conducted to investigate the influence of viscosity on temperature, excess pore pressure, and displacement. It is shown that viscosity has little influence on temperature, a modest influence on displacements, and a quite significant influence on excess pore pressure.     

Dynamic motion and tension of marine cables being laid during velocity change of mother vessels

Flexible segment model （FSM） is adopted for the dynamics calculation of marine cable being laid. In FSM, the cable is divided into a number of flexible segments, and nonlinear governing equations are listed according to the moment equilibriums of the segments. Linearization iteration scheme is employed to obtain the numerical solution for the governing equations. For the cable being laid, the payout rate is calculated from the velocities of all segments. The numerical results are shown of the dynamic motion and tension of marine cables being laid during velocity change of the mother vessels.     

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.     

Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

The paper studies the parametric stochastic roll motion in the random waves. The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed. Random sea surface is treated as a narrow-band stochastic process, and the stochastic parametric excitation is studied based on the effective wave theory. The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function. By using the stochastic averaging method, the differential equation of motion is transformed into Ito's stochastic differential equation. The steady-state probability density function of roll motion is obtained, and the results are validated with the numerical simulation and model test.