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.

Effects of Second-Order Difference-Frequency Wave Forces on Floating Wind Turbine Under Survival Condition

In this paper, the effects of second-order difference-frequency wave forces on the global motion of an offshore wind turbine system with a large displacement under the survival condition are studied. In this case, the hydrodynamic force is the main force because the blades are feathered to reduce the lifting force. The first-order hydrodynamic forces are calculated by WADAM, while the second-order wave forces are calculated by a customized MATLAB module. Then the hydrodynamic coefficients are transferred to the wind turbine analytical code FAST. Through the comparisons of dynamic responses between the first- and second-order numerical models, it is found that the second-order wave forces significantly influence the motion of floating wind turbine under the survival condition. Moreover, neglecting the second-order force significantly underestimates the tension forces in the mooring lines. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.

Second-Order Potentials and Forces for Two-Dimensional Diffraction Problem of Finite Water Depth

-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.

AN ANALYTICAL SOLUTION OF SECOND－ORDER WAVE FORCE ON A VERTICAL CIRCULAR CYLINDER

So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

A SECOND ORDER STATIONARY SOLUTION OF THE THREE DIMENSIONAL WAVE DIFFRACTION POTENTIAL

A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.

SECOND-ORDER INTERACTION OF IRREGULAR WAVES WITH A TRUNCATED COLUMN

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.

SQUEEZE FLOW OF A SECOND-ORDER FLUID BETWEEN TWO PARALLEL DISKS OR TWO SPHERES

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

Theory and application of numerical simulation method of capillary force enhanced oil production

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced （chemical） oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.

浮式风力机若干特征动力学问题综述

总结浮式风力机类型及其对应的特征动力学问题,针对浮式风力机气动荷载、水动荷载的计算方法以及结构动力学、控制动力学典型问题进行论述。讨论了气动—水动—结构—伺服耦合分析的难点,重点分析了二阶波浪力、畸形波等非线性波浪荷载、流荷载及涡激运动对浮式风力机特征动力响应的影响。阐述了浮式风力机动力学研究的试验方法、数值仿真方法、样机测试方法,并对模型试验技术的相似理论、气动模型的实现和难点以及数值仿真的频域方法、时域方法和分析工具进行了归纳对比。研究表明:浮式风力机多场、多体耦合动力分析机理及相关技术仍不成熟,气动荷载、高阶非线性波浪荷载耦合模型的建立是动力学问题研究的重点,数值仿真及模型试验是浮式风力机动力响应研究的主要方法,样机测试技术的积累将促进设计标准的完善及浮式风电的产业化发展。

h型双排桩在山地建筑边坡工程中应用

针对山地建筑边坡受用地限制而常用挡墙不太适用的问题,提出了h型双排桩结构形式,其由冠梁、腰梁、盖板、前排桩及后排桩组成。首先,假定h型双排桩的上部山体为滑裂体,采用传递系数法计算剩余下滑力,与双排桩抗滑力进行比较,判断边坡整体稳定性;假定h型双排桩为悬臂二阶柱结构,计算结构变形,判断变形是否满足正常使用要求。其次,依托某边坡工程进行实例论证,该工程竣工已近两年,监测数据表明边坡处于安全稳定可控状态。最后,h型双排桩解决了山地建筑边坡用地受限的难题,双排桩强有力的结构形式提高了悬臂式挡土高度,且双排桩盖板可兼作山地建筑的室外用地使用。

二阶波浪力对浮式风机系统动力响应的影响研究

文中以OC4-DeepCwind海上浮式风机系统为例,考虑浮式基础运动与气动力之间的耦合,研究了二阶波浪力对浮式风机系统动力响应的影响.结果表明:二阶波浪力增加了浮式基础纵荡和纵摇运动的标准差,而浮式基础纵荡和纵摇对风机气动力有较大的影响,从而使得风轮的推力及功率波动都增大.因此,在风力机系统控制设计及风力机叶片结构设计时,需要充分考虑二阶波浪力的影响.此外,二阶和频力和塔柱一阶固有频率接近,激发了塔柱自振,在设计塔柱时应避开二阶和频力.

基于参数自适应的RSSD-CYCBD及在轴承外圈故障特征提取中的应用

针对滚动轴承工作环境复杂、故障特征信号易被高强度噪声掩盖的问题,提出了基于参数自适应的共振稀疏分解(RSSD)和最大二阶循环平稳盲解卷积(CYCBD)的滚动轴承故障诊断方法。首先,利用人工大猩猩部队优化算法(GTO),结合相关系数与相关峭度的融合指标,自适应选择RSSD分解参数,得到了仿真信号的最优低共振分量;然后,利用GTO结合包络熵,自适应选择CYCBD的循环频率和滤波器长度,对最优低共振分量进行了解卷积运算,从包络谱中获得了信号的故障特征频率;最后,利用美国凯斯西储大学试验台和MFS-MG机械故障综合模拟试验台数据,综合验证了该方法的有效性,并将试验结果与RSSD-MCKD方法的结果进行了对比。研究结果表明,该方法能够准确地得到仿真信号的故障频率为20 Hz、美国凯斯西储大学试验台近似故障频率为107.5 Hz、MFS-MG试验台近似故障频率为87.6 Hz。自适应RSSD-CYCBD方法能够有效地识别出故障特征频率及其倍频,实现滚动轴承故障诊断的目的。

SECOND ORDER DIFFRACTION FORCES ON HORIZONTAL CYLINDERS

The second order diffraction forces on a floating semicircular cylinder and a submerged circular cylinder are calculated using the method of Lighthill(ref.3). The first order potential is obtained by the multipole expansion and numerical results are provided.

FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES

At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.

A NUMERICAL METHOD FOR SECOND ORDER MEAN FORCES AND SLOWLY VARYING FORCES ON A FLOATING STRUCTURE

Existing far field expressions of second order potentials are by no means complete.Hence there has been no exact far field expression of second order potentials.In this paper the far field expression for Φ_d^((2)) is purposely avoided in deducing the formulae of second order forces and a series of functions Φ_(dRn)^((?)) are used.The far field expression of is given,which for (x,U,z)∈Σ,φ_(dRn)^((2))(?) φ_d^((2)).Using these properties formulae for calculating second order diffraction forces are obtained.To calculate the integral ∫∫_(?)1/g f_(?)Ψ_(?)ds it is divided into two parts.One is the integral over a finite domain and the function under the integral is continuous,so the usual approximate integration formulae may be used. The other is the integral over an infinite domain.Using the far field expression of first order potentials,formulae for calculating the integral to meet given accuracies are given. The mooring force in surge direction is used for comparison between numerical predictions and experimental measurements.The predicted results are checked against the measured value in a specially designed test.In the low frequency domain of interest,the mooring forces in surge,for calculated and experimental spectra are in good consistency so long as the damping coefficients is choosen appropriately.

基于内摆线原理设计的四缸汽油发动机惯性力分析

使用曲柄连杆机构的传统四缸汽油发动机在运行时会产生二阶往复惯性力,导致发动机的振动较大。为了解决该问题,基于内摆线原理设计出一种新型四缸汽油发动机。对该发动机的惯性力进行了理论分析,并使用Adams软件进行了仿真验证。结果表明:四缸内摆线汽油发动机在一阶往复惯性力和旋转惯性力达到平衡的同时,不会产生二阶往复惯性力,有效降低了发动机的振动。

海洋浮体二阶非线性水弹性力学分析—基本理论

将考虑到二阶的流场压力在浮体瞬时湿表面上积分 ,得到用于非线性水弹性理论分析的广义一阶流体作用力和广义二阶流体作用力。广义一阶流体作用力中的波浪激励力、辐射力和恢复力与线性水弹性理论中的广义流体力具有相同的形式 ,仅比线性水弹性理论多了一项 ,反映了由刚体的转动引起的对一阶流体恢复力的影响。广义二阶流体力由五部分组成 ,即 :与入射势和反射势有关的广义二阶波浪激励力、与辐射势有关的广义二阶辐射力、由辐射势与入射势及反射势的耦合引起的广义二阶力、由于湿表面的移动引起的一阶流场静态压力对广义二阶流体力的贡献、以及由于瞬时湿表面积的变化引起的广义二阶力。同时推导了不规则波中的广义一阶及二阶流体动力系数的表达形式。建立了在不规则波中航行浮体的线性和非线性水弹性运动方程 ,给出了求解方法。

潜体近水面波浪力计算的数值方法

潜体近水面航行时将受到波浪力的作用．其中二阶垂向平均力和二阶纵摇平均力矩有可能使潜体浮出水面，因此正确估算作用在潜体上的二阶平均波浪力．对近水面航行的潜体十分重要。本文利用波浪上任意低航速三维物体波浪力的计算方法来计算近水面潜体的波浪力并与国际上椭球计算结果、试验结果相比比较吻合，说明了本方法的实用性。

双色入射波下二阶波浪力响应函数

应用边界元方法，对双频入射波在和频及差频下的二阶速度势做了完整的求解，通过物面积分计算了任意三维结构上的二阶波浪力的传递函数．对简单几何物体，与发表的结果做了对比，两者吻合良好，验证了本方法的正确性．应用这一方法还对复杂的张力腿平台模型做了实际计算，发现在低频和高频区二阶波浪力平方响应函数有着显著的能量分布．