Heave-roll-pitch coupled nonlinear internal resonance response of a spar platform considering wave and vortex exciting loads

Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model. In fact, in addition to the heave and pitch which are in one plane, the nonlinear unstable motion will also occur in roll. From the results of the experiments, the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch. The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force. The nonlinear coupled equations in heave, roll and pitch are established by considering time-varying wet surface and coupling. The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency. Numerical integration of the motion equations has been performed to verify the first-order perturbation solution. The results are confirmed by model test. There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch. It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value. The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch. The energy transfers from heave to pitch and then transfers from pitch to roll. Due to the influence of the low-frequency vortex-excited force, the response of roll is more complicated than that of pitch.     

用随机有限断层方法模拟2016-11-13新西兰Mw7.8地震

在未来大地震发震构造已知的前提下,提出用经验公式确定大地震断层长度、宽度、地震矩和滑动分布等参数,并用随机有限断层方法预测未来大地震。用随机有限断层方法模拟2016-11-13新西兰M_W7.8地震的12个基岩台站地震动时程和反应谱,并用模拟的频谱幅值与记录频谱幅值平均比值确定模拟误差。结果表明,在周期为0~10 s的范围内,模拟误差在0.92~1.08之间,不同频率模拟误差的标准差变化范围不超过1。95%的置信区间宽度随频率无明显变化,模拟结果反映了地震动记录的平均效果。用准随机方法重新获取新西兰大地震断层初始破裂点和位错滑动分布,模拟地震动并计算模拟误差随频率的变化,得到与最初模型相似的结论,从而进一步证实了本文提出的获取震源参数并用随机有限断层方法预测未来大地震的可靠性,且其特别适用于大地震远场模拟。     

Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.     

Finite water depth effect on wave-body problems solved by Rankine source method

Finite water depth effect for wave-body problems are studied by continuous Rankine source method and non- desingularized technique. Free surface and seabed surface profiles are represented by continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the fluid boundary surfaces and therefore no desingularization technique is required. Space increment method is applied for both free surface source and seabed source arrangements to reduce computational cost and improve numerical efficiency. Fourth order Runge-Kutta iteration scheme is adopted on the free surface updating at every time step. The finite water depth effect is studied quantitatively for a series of cylinders with different B/T ratios. The accuracy and efficiency of the proposed model are validated by comparison with published numerical results and experimental data. Numerical results show that hydrodynamic coefficients vary for cylinder bodies with different ratios of B/T. For certain set of B/T ratios the effect of finite water depth increases quickly with the increase of motion frequency and becomes stable when frequency is relatively large. It also shows that water depths have larger hydrodynamic effects on cylinder with larger breadth to draft ratios. Both the heave added mass and damping coefficients increase across the frequency range with the water depths decrease for forced heave motion. The water depths have smaller effects on sway motion response than on heave motion response.     

Probabilistic analysis and fatigue damage assessment of offshore mooring system due to non-Gaussian bimodal tension processes

Both wave-frequency (WF) and low-frequency (LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system. This paper conducts a comprehensive investigation of applicable probability density functions (PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method. Short-term statistical characteristics of mooring-line tension responses are firstly investigated, in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients. Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes. Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components. A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses. Using time domain simulation as a benchmark, its accuracy is further validated using a numerical case study of a moored semi-submersible platform.     

Dynamic performance of a semi-submersible platform subject to wind and waves

By applying experimental and numerical simulations, the motion performance of a semi-submersible platform with mooring positoning system under combined actions of wind and waves is studied. The numerical simulation is conducted by the method of nonlinear time domain coupled analysis, and the mooring forces are calculated by the piecewise extrapolating method. The scale in the model experiment is 1:100, and the mooring system of the model is designed with the method of equivalent water-depth truncation by comparing the numerical and the experimental results, the platform motion and mooring forces subject to wind and waves are investigated. The results indicate that the numerically simulated mooring forces agree well with the experimental results in static equivalent field, but show some difference in dynamic equivalent field; the numerically simulated platform motions coincide well with the experimental results. The maximum motion of the platform under operating conditions is 20.5 m. It means that the horizontal displacement is 2% less than the water depth, which satisfies the operating requirements.     

Parametric Instability Analysis of Deepwater Top-Tensioned Risers Considering Variable Tension Along the Length

Parametric instability of a riser is caused by fluctuation of its tension in time due to the heave motion of floating platform. Many studies have tackled the problem of parametric instability of a riser with constant tension. However, tension in the riser actually varies linearly from the top to the bottom due to the effect of gravity. This paper presents the parametric instability analysis of deepwater top-tensioned risers(TTR) considering the linearly varying tension along the length. Firstly, the governing equation of transverse motion of TTR under parametric excitation is established. This equation is reduced to a system of ordinary differential equations by using the Galerkin method. Then the parametric instability of TTR for three calculation models are investigated by applying the Floquet theory. The results show that the natural frequencies of TTR with variable tension are evidently reduced, the parametric instability zones are significantly increased and the maximum allowable amplitude of platform heave is much smaller under the same damping; The nodes and antinodes of mode shape are no longer uniformly distributed along the axial direction and the amplitude also changes with depth, which leads to coupling between the modes. The combination resonance phenomenon occurs as a result of mode coupling, which causes more serious damage.     

Hydroelastic Analysis of a Very Large Floating Structure Edged with a Pair of Submerged Horizontal Plates

This paper is concerned with the hydroelastic problem of a very large pontoon-type floating structure(VLFS) edged with a pair of submerged horizontal plates, which is a combination of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. For the hydroelastic analysis, the fluid is assumed to be ideal and its motion is irrotational so that a velocity potential exists. The VLFS is modeled as an elastic plate according to the classical thin plate theory. The fluid-structure interaction problem is separated into conventional hydrodynamics and structure dynamics by using modal expansion method in the frequency-domain. It involves, firstly, the deflection of the VLFS, which is expressed by a superposition of modal functions and corresponding modal amplitudes. Then the boundary element method is used to solve the integral equations of diffraction and radiation on the body surface for the velocity potential, whereas the vibration equation is solved by the Galerkin’s method for modal amplitudes, and then the deflection is obtained by the sum of multiplying modal functions with modal amplitudes. This study examines the effects of the width and location of the non-perforated horizontal plates on the hydroelastic response of the VLFS, then the performance of perforated plates is investigated to reduce the motion near the fore-end of the VLFS. Considering the advantages and disadvantages of submerged plates without and with cylindrical holes, we propose a simple anti-motion device, which is a combination of a pair of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. The effectiveness of this device in reducing the deformation and bending moment of the VLFS has been confirmed, and is compared with the results in cases without and with the submerged horizontal plates by the analysis in this paper.     

基于Levenberg-Marquarat算法的非线性三维直角坐标转换方法

提出一种基于Levenberg-Marquarat算法的非线性三维直角坐标转换方法,在法矩阵病态或者奇异时依然有效,并通过修正旋转角参数的方法,有效解决了平移量与旋转角量纲不同造成的迭代发散问题。设计出简洁有效的迭代求解模式,获得了稳定的参数解。最后通过模拟数据对比分析,证明该方法的有效性和正确性。     

基于单齿侵入理论的牙轮钻头钻速方程

考虑井底水平地应力、钻井流体压力及地层孔隙压力,基于单齿侵入理论推导单齿侵入井底岩石的侵深公式,建立纯滚动锥形齿、楔形齿和滚动、剪切复合运动锥形齿等牙轮钻头的钻速方程.通过实验分析刃尖角、井底液柱压力对单齿侵入深度的影响,以及转速、轴向载荷对微钻头、牙轮钻头机械钻速的影响.结果表明:随着牙齿刃尖角的增大,锥形齿和楔形齿的侵深呈指数递减趋势;随着井底液柱压力的增大,牙齿侵入深度呈指数递减趋势,其中锥形齿降低速率大.在软到中硬地层中,牙齿侵入深度大,冲击侵入、回转剪切复合破岩方式的破岩效率高;在硬度地层中,牙齿侵入深度小,纯滚动冲击侵入破岩效率高.为分析实钻时牙轮钻头的机械钻速提供计算方法.     

CRInSAR与PSInSAR融合探测地表线性变形速率

提出利用CRInSAR与PSInSAR融合解算地表变形参数的算法。将CR点上获取的线性变形速率与高程改正结果作为PS基线网络的起算数据,依据最小二乘原理求解PS点上待求线性变形速率与高程改正值的最优解。这一算法可融合PSInSAR与CRInSAR两种算法的优势,起到很好的互补作用。实验显示,这一算法获取的线性变形速率精度可达±0.37 mm/a,高程改正值精度可达±0.5 m,证实该算法在实际地表变形监测中具备可行性。     

联合GRACE卫星轨道及距离变率数据反演地球重力场方法研究

基于动力学法,研究联合GRACE卫星精密轨道及距离变率数据反演地球重力场的方法,该方法可对重力位系数及卫星初始状态误差同时进行有效校正。通过对各观测值模拟不同的随机误差,研究了不同精度观测值联合反演所能达到的精度,以及用相同精度的观测值进行联合反演时不同采样率对反演结果的影响,模拟计算结果表明：联合反演模式下,当距离变率精度为1 μm/s,卫星位置精度为2~3 cm,速度精度为0.1~0.5 mm/s时,加速度计精度为(1.0×10 ^-10~1.0×10^-9 m/s ²比较适合;将距离变率精度由1 um/s提高到0.1 um/s时,反演精度可获得相应提高;在观测值精度一定的情况下,联合反演算法宜采用5 s采样率。     

On the nonlinear waves in a developing process

Based on the discrete form of the main governing equation derived, a single wave as the main motion of the instability analysis was found. This solution gives the whole process from the initial stage to the nonlinear equilibrium state. Next we examined the instability of the main motion above-mentioned in the initial stage and showed the instability properties of a developing process. Contribution No. 987 from the Institute of Oceanology, Academia Sinica.     

一种基于改进外点法的多项式拟合解法

针对多项式模型拟合的参数求解问题,依据最优化方法理论,将其转化为有约束的非线性规划问题进行求解,采用最速下降法进行迭代,从而在不线性化的情况下解决非线性问题。首先通过分析外点法的罚因子、目标函数和迭代初值,说明对外点法改进的合理性;再通过算例,说明该方法的可行性,并与常规方法比较,显示出其精度高、多解性等优点,为研究非线性模型空间数据处理理论提供一种新的思路。     

地表组合粗糙度不确定性引起的SAR反演土壤水分的不确定性分析

地表粗糙度的不确定性是引起SAR土壤水分反演结果不确定性的主要因素,现有研究大多着重于研究单个粗糙度参数（主要是相关长度）的不确定性,直接研究地表组合粗糙度不确定性的较少。本文使用偏度、峰度和四分位距3个指标来量化不确定性,通过在组合粗糙度中加入不同量级高斯噪声进行随机扰动的方法,研究组合粗糙度不确定性在反演过程中的传递,并对反演土壤水分的不确定性进行定量分析。进一步研究反演土壤水分的均方根误差对组合粗糙度不同比例误差范围的响应特征,得到满足反演精度要求的组合粗糙度误差控制范围。样区的实验分析结果表明：组合粗糙度高斯噪声标准差在0-0.045之间时,峰度取值从-0.1984到1.2501,偏度取值从0.0191到0.6791,四分位距取值从0.0018到0.0167,3个量化指标都随组合粗糙度高斯噪声量级的增大而增大,土壤水分反演值有集中在众数附近的趋势,土壤水分低估倾向比高估倾向更明显;本文提出的组合粗糙度误差控制范围可满足反演精度要求,误差控制范围与入射角负相关。     

The Coupling VIV Analysis of SCRs with Rigid Swing

With the development of deepwater oil and gas exploration, Steel Catenary Risers(SCRs) become preferred risers for resource production, import and export. Vortex induced vibration(VIV) is the key problem encountered in the design of SCRs. In this study, a new model, the rigid swing model, is proposed based on the consideration of large curvature of SCRs. The sag bend of SCRs is assumed as a rigid swing system around the axis from the hanging point to the touch down point(TDP) in the model. The torque, produced by the lift force and the swing vector, provides the driving torque for the swing system, and the weight of SCRs provides the restoring torque. The simulated response of rigid swing is coupled with bending vibration, and then the coupling VIV model of SCRs is studied in consideration of bending vibration and rigid motion. The calculated results indicate that the rigid swing has a magnitude equal to that of bending vibration, and the rigid motion affects the dynamic response of SCRs and can not be neglected in the VIV analysis.     

九寨沟MS7.0地震强地震动模拟及参数敏感性分析

对2017年九寨沟M_S7.0地震进行强地面运动模拟,应用复合震源模型建立特定圆形子震分布的断层破裂运动学模型,对地震矩、应力降、破裂速度、子断层尺寸和震源深度等参数进行敏感性分析,得到一组合理的震源参数,然后基于复合震源模型计算得到该地区地震动,最后与观测的峰值加速度(PGA)、反应谱和PGA的空间分布特征进行对比。结果表明,该模型整体上可以再现各台站地震动强度特征,验证了复合震源模型计算强地面运动的有效性,同时敏感性规律也为复合震源模型计算缺乏强震记录区域的地震动参数的变化区间提供了依据。     

Numerical study on inter-tidal transports in coastal seas

Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian in- ter-tidal concentration(LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is nu- merically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as ‘flat-bottom', ‘stairs' and ‘cape' case, re- spectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the ‘flat-bottom' case still meets the convectively weakly nonlinear condi- tion. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the de- pendence of the LIS(Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coast- lines, and that in the latter region is due to the presence of the estuarine salinity front.     

Time domain Rankine-Green panel method for offshore structures

To solve the numerical divergence problem of the direct time domain Green function method for the motion simulation of floating bodies with large flare, a time domain hybrid Rankine-Green boundary element method is proposed. In this numerical method, the fluid domain is decomposed by an imaginary control surface, at which the continuous condition should be satisfied. Then the Rankine Green function is adopted in the inner domain. The transient free surface Green function is applied in the outer domain, which is used to find the relationship between the velocity potential and its normal derivative for the inner domain. Besides, the velocity potential at the mean free surface between body surface and control surface is directly solved by the integration scheme. The wave exciting force is computed through the convolution integration with wave elevation, by introducing the impulse response function. Additionally, the nonlinear Froude-Krylov force and hydrostatic force, which is computed under the instantaneous incident wave free surface, are taken into account by the direct pressure integration scheme. The corresponding numerical computer code is developed and first used to compute the hydrodynamic coefficients of the hemisphere, as well as the time history of a ship with large flare; good agreement is obtained with the analytical solutions as well as the available numerical results. Then the hydrodynamic properties of a FPSO are studied. The hydrodynamic coefficients agree well with the results computed by the frequency method; the influence of the time interval and the truncated time is investigated in detail.     

Landslide dynamic process and parameter sensitivity analysis by discrete element method: the case of Turnoff Creek rock avalanche

The great diversity and complexity of geological hazards in terms of flowing materials, environment, triggering mechanisms and physical processes during the flow bring great difficulties to the numerical parameter selection for the discrete element method. In order to identity the significance of individual parameters on the landslides dynamic process and provide valuable contribution to the runout analysis of similar landslide, the dynamic process and associated microscopic mechanism of the Turnoff Creek rock avalanche in Canada are simulated. The present numerical results are compared with the field survey data and the results of depth-integrated continuum method. The final deposit range matches well with the field survey data. It is illustrated that the discrete element method is robust and feasible to capture the dynamic characteristics of large rock avalanche over a complex terrain. Besides, a new method to assess the landslide hazard level based on the discrete element method is proposed. According to the parameter sensitivity analysis, it is demonstrated that the basal friction coefficient and bond strength are essential to the final deposit while rolling coefficient and restitution coefficient have little effects on it.