On the parametric excitation of vertical elastic slender structures and the effect of damping in marine applications

The dynamic behaviour of vertical slender structures for marine applications under parametric excitation is considered. The governing equations are treated using two different numerical schemes. The effect of parametric excitation is examined in cases where the excitation frequency lies in the vicinity of nonlinear resonances. First, the un-damped case is considered and the features of the dynamic response are properly identified and discussed. For explaining the particulars of the un-damped behaviour, the governing equations are treated analytically by applying the method of normal forms. The effect of damping is examined through comparative numerical computations of the system's behaviour. It is shown that the inclusion of hydrodynamic drag in the describing model eliminates the impacts of internal resonances excited due to the parametrically imposed motions. Finally, the paper demonstrates the significance of the terms that describe the coupling between the longitudinal and transverse vibrations.     

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.     

深海采矿转场工况平台—水下系统耦合动力响应特性研究

针对水深6.0 km深海采矿装备,研究其转场工况平台—水下系统耦合动力响应特性。建立深海采矿平台—输浆管—中继站一体化耦合动力模型,其中采用有限元方法离散输浆管,采用势流理论计算平台水动力,基于Kalman滤波对动力定位系统进行参数整定,优化动力定位系统推力。考虑动力定位系统,计算水动力和采矿平台—输浆管—中继站的频域响应和平台—水下系统耦合时域运动响应,计算得到了平台时域运动响应、水下系统动力响应及动力定位系统推力响应。结果表明：建立的一体化耦合动力分析模型是可行的,可以有效预报平台及水下系统响应;转场0°浪向动力定位系统可以有效控制平台运动;中继站运动较小,输浆管轴力较大,建议将输浆管的浮力材料移动到流速较小的水下范围,可降低拖曳力,有利于输浆管的强度性能。     

Hill Instability Analysis of TLP Tether Subjected to Combined Platform Surge and Heave Motions

This paper presents the Hill instability analysis of Tension keg Platform （TLP） tether in deep sea. The 2-D nonlinear beanl model, which is undergoing coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin＇ s method and the modes superposition principle. The Hill instability charted up to large parameters is obtained. An important parameter M is defined and can be expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various envirotnnental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure. It needs to be considered for the accurate dynamic analysis of long TI2 tether subjected to the combined platfolna surge and heave motions.     

Heave response of long riserless drill strings

The sensitivity of heave response predictions for long riserless drill strings hanging from a floating vessel are examined. A general analytical procedure is presented which is suitable for a variety of deepwater pipe systems. The dynamic response behavior is characterized in terms of the dynamic magnification, phase angle and total stress. The examples presented here focus on drill string systems, which vary in length from 9000 ft (2743 m) to 27,000 ft (8230 m) and can include a large package to be lowered to the seafloor. A procedure for evaluating the undamped natural periods and the corresponding mode shapes is presented. The sensitivity of the natural period estimates to hydrodynamic added mass approximations is examined. Numerical results for both design wave and random sea simulations are used to illustrate the sensitivity of the dynamic response in near resonant conditions and the possibility of exciting higher modes for very long riserless drill string systems. Finally, the sensitivity of the displacement predictions to reasonable variations in skin friciton and viscous drag coefficients are presented and discussed.     

A hybrid time/frequency domain approach for efficient coupled analysis of vessel/mooring/riser dynamics

The dynamic analysis of a deepwater floating structure is complex due to dynamic coupling between the platform and the moorings/risers. Furthermore, the system response at the incident wave frequency and at the resonant low frequency is coupled due to geometric and hydrodynamic nonlinearities. As such, it is generally held that a fully coupled time-domain analysis should be used for an accurate prediction of the dynamic response. However, in a recent work, it is found that for an ultra-deepwater floating system, a fully coupled frequency-domain analysis can provide highly accurate response predictions. One reason is the accuracy of the drag linearization procedure over the motions at two time scales, another is the minimal geometric nonlinearity of the moorings/risers in deepwater. In this paper, the frequency-domain approach is investigated for intermediate water depths, and it is found that the accuracy reduces substantially as geometric nonlinearity becomes important. Therefore, a novel hybrid approach is developed, in which the low-frequency motion is simulated in the time domain while the wave frequency motion is solved in the frequency domain at regular intervals. Coupling between the two analyses is effected by the fact that (i) the low-frequency motion affects the line geometry for the wave frequency motion, and (ii) the wave frequency motion affects the modeling of the drag forces, which damp the low-frequency motion. The method is found to be nearly as accurate as fully coupled time domain analysis even for a system with a preponderance of nonlinear and coupling effects, but requiring only one-tenth of the computational effort.     

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.     

Spar平台垂荡-纵摇耦合运动失稳机理

研究参数激励和强迫激励共同作用下Spar平台垂荡-纵摇耦合运动的失稳机理.考虑静稳性和排水体积的变化,推导平台的垂荡回复力和纵摇回复力矩表达式,建立规则波浪中平台垂荡-纵摇耦合的运动方程.以经典Spar平台为例,分析平台垂荡-纵摇耦合运动发生马休类型不稳定运动的条件以及平台运动失稳的形式,给出波高和波浪周期平面上平台因大幅运动失稳的参数域.结果表明,当波高相对较小时,波浪的临界周期接近于垂荡固有周期,平台失稳的形式为马休失稳;当波高相对较大时,波浪的临界周期远离垂荡固有周期,平台由于大幅摇摆运动而失稳.     

Influence of yaw-roll coupling on the behavior of a FPSO: An experimental and numerical investigation

An inconvenience in the experimental set-up of a FPSO in regular waves highlighted occurrence of parametric-roll events promoted by yaw-roll coupling and motivated a combined physical and numerical analysis on the relevance of this phenomenon on the roll resonance, as well as on the water shipping. The model tests examine the ship in head- and bow-sea waves in the zone of the first parametric resonance. Numerically, it is adopted a 3D Domain-Decomposition (DD) strategy combining a weakly-nonlinear potential-flow solver based on the weak-scatterer theory with a shallow-water approximation for the shipped liquid and with a bottom-slamming solution. Detailed comparisons against these and other seakeeping experiments validated the numerical method in its different aspects with global success.At first, a 2-dof equivalent linearized yaw-roll coupled system is examined and the measurements are used to estimate hydrodynamic coefficients required to complete the mathematical model of the problem. Then the DD method is applied to verify the instability occurrence and compared against the experiments. From the analysis, the parametric-roll instability does not occur if all nonlinearities in the roll restoring load are not accounted for. However the amplitude of the resonant roll is affected by the coupling with the other degrees of freedom. Especially the coupling with yaw tends to increase the steady-state roll amplitude. It also affects the water shipping with the trend in reducing its severity for the vessel, this is opposite to the influence of the parametric roll in head-sea waves on the water on deck, as documented in Greco et al. (2014) [4].     

Experimental Investigation on Vortex-Induced Vibration of Deep-Sea Risers of Different Excitation Water Depths

The vortex-induced vibration test of the deep-sea riser was carried out with different excitation water depths in the wave-current combined water flume.By dimensionally changing the multi-stage water depth and hydrodynamic parameters such as outflow velocity at various water depths,the dynamic response parameters such as dominant frequency,dimensionless displacement and vibration trajectory evolution process of the riser under different excitation water depths were explored to reveal the sensitive characteristics of the dynamic response of vortexinduced vibration of the risers under different excitation water depths.The results show that different excitation water depths will change the additional mass of the riser and the fluid damping and other parameters,which will affect the spatial correlation and stability of the vortex shedding behind the riser.In the lock-in region,the distribution range of the characteristic frequency becomes narrow and centered on the lock-in frequency.The increase of the excitation water depth gradually advances the starting point of the lock-in region of the riser,and at the same time promotes the excitation of the higher-order vibration frequency of the riser structure.Within the dimensionless excitation water depth,the dominant frequency and dimensionless displacement are highly insensitive to the excitation water depth at high flow velocity.The change of the excitation water depth will interfere with the correlation of the non-linear coupling of the riser.The“8-shaped”gradually becomes irregular,and the vibration trajectories of the riser show“O-shape”,“X-shape”and“Crescent-shape”.     

Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.     

Tension during parametric excitation in submerged vertical taut tethers

The construction of a suspension bridge with floating pylons or a submerged floating tunnel requires the installation of a mooring system. The option of taut vertical tethers, similar to those used in tension-leg platforms, has been suggested in preliminary designs. The environmental loading on the tether, mainly due to wind waves and swell, results in a parametrically excited system. Certain loading conditions develop instabilities that translate into large horizontal motion. However, the effects of parametric resonance on the tension values have rarely been investigated. This paper aims to clarify the relation between lateral displacement and tether tension and to quantify the extreme tension values in the event of parametric resonance. The presented analysis is based on a full numerical model of the tether that includes geometric and hydrodynamic nonlinear effects. This model is used to investigate a representative example that illustrates parametric resonance and multiple parametric studies to assess the effects of the excitation frequency, amplitude, initial pretension, tether length and inclination angle on the tether’s response. The results reported here provide the basis for a recommendation on designing a tether under parametric resonance regarding the ultimate extreme values and fatigue life.     

Vibration induced in towed linear underwater array cables

Towed linear arrays of hydrophones are used in various applications, for example, seismic prospecting. Tow cable vibration is capable of causing output in the towed array system. Since one of the factors limiting acoustic sensitivity is self-noise, the general objective of this analysis is to investigate the nature of longitudinal and transverse cable vibrations, with the aim of minimizing vibration transmitted to the array. The equations of transverse cable motion are derived and solved for a single-póint excitation and for distributed-vortex excitation. The response to vortex-shedding excitation along the first 150 ft of array-end cable is quantitatively evaluated and compared with actual tow-trial measurements. Two types of longitudinal vibration are analyzed, one caused by direct excitation along the cable axis, and one caused indirectly by transverse cable vibration. Fluid drag and hysteretic damping are included in the analysis.     

Instability Assessment of Deep-Sea Risers Under Parametric Excitation

This study deals with the nonlinear dynamic response of deep-sea risers subjected to parametric excitation at the top of a platform.As offshore oil and gas exploration is pushed into deep waters,difficulties encountered in deep-sea riser design may be attributed to the existence of parametric instability regarding platform heave motions.Parametric resonance in risers can cause serious damage which might bring disastrous accidents such as environment pollution,property losses and even fatalities.Therefore,th...     

Coupled analysis for response and instability of sloping seabed under wave action

Wave-induced instability of seabed may cause damage to coastal and offshore structures. This issue has been investigated mostly for mildly sloping ($<5^{°}$) seabed considering uncoupled or one-way coupled response of wave and seabed interaction. However, some of the marine structures are founded on seabed with steeper slopes. In this study, the wave-induced response and instability of sloping seabed are evaluated using a coupled finite element model. The interaction between fluid and porous seabed accounting for the effect of fluid motion on the seabed response, and conversely the effect of seabed response on the fluid motion (but not on the surface wave profile) is considered. The results indicate that the system response (fluid pressure, stresses, etc.) and the extent of instantaneously liquefied zone within the sloping seabed with significant steepness are lesser than those for horizontal seabed. Moreover, for typical sediment and wave characteristics, for the flat seabed, the response obtained from fully coupled analysis is not significantly different from those obtained by uncoupled analysis. For the sloping bed, such difference is slightly greater as compared to that for the flat bed.     

Hybrid Analysis Approach for Stochastic Response of Offshore Jacket Platforms

The dynamic response of offshore platforms is more serious in hostile sea environment than inshallow sea.In this paper,a hybrid solution combined with analytical and numerical method is proposedto compute the stochastic response of fixed offshore platforms to random waves,considering wave-struc-ture interaction and non-linear drag force.The simulation program includes two steps:the first step is theeigenanalysis aspects associated the structure and the second step is response estimation based on spectralequations.The eigenanalysis could be done through conventional finite element method conveniently andits natural frequency and mode shapes obtained.In the second part of the process,the solution of theoffshore structural response is obtained by iteration of a series of coupled spectral equations.Consideringthe third-order term in the drag force,the evaluation of the three-fold convolution should be demanded fornonlinear stochastic response analysis.To demonstrate this method,a numerical analysis is carrie     

抑制涡激振动的螺旋列板设计参数研究

基于水池模型实验结果和工程设计经验,结合国内外试验数据,着重分析用于抑制海洋立管涡激振动的螺旋列板几何参数(鳍高和螺距)及覆盖率对立管涡激振动的影响;并对水动力直径和水动力系数的选取对预报涡激振动的影响进行了分析,进而提出了适合于海洋立管工程应用的螺旋列板几何和设计参数选取的建议,为螺旋列板工程应用、海洋立管强度和疲劳设计提供参考。     

Dynamic Analysis of A 5-MW Tripod Offshore Wind Turbine by Considering Fluid–Structure Interaction

Fixed offshore wind turbines usually have large underwater supporting structures. The fluid influences the dynamic characteristics of the structure system. The dynamic model of a 5-MW tripod offshore wind turbine considering the pile–soil system and fluid structure interaction (FSI) is established, and the structural modes in air and in water are obtained by use of ANSYS. By comparing low-order natural frequencies and mode shapes, the influence of sea water on the free vibration characteristics of offshore wind turbine is analyzed. On basis of the above work, seismic responses under excitation by El-Centro waves are calculated by the time-history analysis method. The results reveal that the dynamic responses such as the lateral displacement of the foundation and the section bending moment of the tubular piles increase substantially under the influence of the added-mass and hydrodynamic pressure of sea water. The method and conclusions presented in this paper can provide a theoretical reference for structure design and analysis of offshore wind turbines fixed in deep seawater.     

考虑弹性变形铰接塔平台非线性动力响应

研究计入弹性变形铰接塔平台在深水中的非线性动力响应。将铰接塔平台简化为顶部具有集中质量,底部具有扭转线性弹簧约束的均匀弹性梁,考虑波浪对平台的作用,应用莫里森(Morison)公式计算铰接塔平台瞬时位置所受水动力,建立了铰接塔平台横向运动的偏微分方程,采用伽辽金方法计算波浪作用下铰接塔平台非线性动力响应。计算了铰接塔平台的固有频率和模态,得到了铰接塔平台不同频率波浪激励下各阶模态的动力响应。计算结果表明,在波浪激励下系统二阶模态将发生2、34、倍超谐共振运动,并且揭示了弹性铰接塔平台在波浪作用下振动的不对称性。     

Dynamic Analysis of A 5-MW Tripod Offshore Wind Turbine by Considering Fluid–Structure Interaction

Fixed offshore wind turbines usually have large underwater supporting structures.The fluid influences the dynamic characteristics of the structure system.The dynamic model of a 5-MW tripod offshore wind turbine considering the pile–soil system and fluid structure interaction(FSI) is established,and the structural modes in air and in water are obtained by use of ANSYS.By comparing low-order natural frequencies and mode shapes,the influence of sea water on the free vibration characteristics of offshore wind turbine is analyzed.On basis of the above work,seismic responses under excitation by El-Centro waves are calculated by the time-history analysis method.The results reveal that the dynamic responses such as the lateral displacement of the foundation and the section bending moment of the tubular piles increase substantially under the influence of the added-mass and hydrodynamic pressure of sea water.The method and conclusions presented in this paper can provide a theoretical reference for structure design and analysis of offshore wind turbines fixed in deep seawater.