Numerical Investigations on Transient Behaviours of Two 3-D Freely Floating Structures by Using a Fully Nonlinear Method

Two floating structures in close proximity are very commonly seen in offshore engineering. They are often subjected to steep waves and, therefore, the transient effects on their hydrodynamic features are of great concem. This paper uses the quasi arbitrary Lagrangian Eulerian finite element method （QALE-FEM）, based on the fully nonlinear potential theory （FNPT）, to numerically investigate the interaction between two 3-D floating structures, which undergo motions with 6 degrees of freedom （DOFs）, and are subjected to waves with different incident angles. The transient behaviours of floating structures, the effect of the accompanied structures, and the nonlinearity on the motion of and the wave loads on the structures are the main focuses of the study. The investigation reveals an important transient effects causing considerably larger structure motion than that in steady state. The results also indicate that the accompanied structure in close proximity enhances the interaction between different motion modes and results in stronger nonlinearity causing 2hal-order component to be of similar significance to the fundamental one.

Study on washability of microcrystal graphite using float-sink tests

This article presented an experimental research on washability of microcrystal graphite using float-sink tests.Chemical and X-ray analyses showed that graphite,semi-graphite,meta-anthracite,and anthracite existed together in this microcrystal graphite sample;and the intergrowth relationship between microcrystal graphite and gangues was very complicated based on optical mineralogy research.The results of float-sink tests revealed that:for the-25+0.5 mm size fraction,about 68%(by weight)of microcrystal graphite was obtained at the density of 2.0 g/cm^3.and the float product met the standard of commercial grade W65;for the-0.5 mm size fraction,58%(by weight)of microcrystal graphite was floated at the density of 2.0 g/cm^3,which met the standard of commercial grade W70.It can be concluded that microcrystal graphite may be upgraded by dense media separation(DMS)providing a float product using as the raw materials of casting or refractories.

An Integrated Structural Strength Analysis Method for Spar Type Floating Wind Turbine

An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.The NREL-5MW ＂Hywind＂ Spar type wind turbine is adopted as study object.Time-domain dynamic coupled simulations are performed by a fully-coupled aero-hydro-servo-elastic tool,FAST,on the purpose of obtaining the dynamic characteristics of the floating wind turbine,and determining parameters for design load cases of finite element calculation.Then design load cases are identified,and finite element analyses are performed for these design load cases.The structural stresses due to wave-induced loads and wind-induced loads are calculated,and then combined to assess the structural strength of the floating wind turbine.The feasibility of the proposed structural strength analysis method for floating wind turbines is then validated.

A Novel Dynamics Analysis Method for Spar-Type Floating Offshore Wind Turbine

The dynamic behavior of floating offshore wind turbine (FOWT) is crucial for its design and optimization. A novel dynamics analysis method for the spar-type FOWT system is proposed in this paper based on the theorem of moment of momentum and the Newton’s second law. The full nonlinearity of the equations of motion (EOMs) and the full nonlinear coupling between external loads and the motions are preserved in this method. Compared with the conventional methods, this method is more transparent and it can be applied directly to the large-amplitude rotation cases. An in-house code is developed to implement this method. The capability of in-house code is verified by comparing its simulation results with those predicted by FAST. Based on the in-house code, the dynamic responses of a spar-type FOWT system are investigated under various conditions.

Rapid prediction of floating and sinking components of raw coal

A model that rapidly predicts the density components of raw coal is described.It is based on a threegrade fast float/sink test.The recent comprehensive monthly floating and sinking data are used for comparison.The predicted data are used to draw washability curves and to provide a rapid evaluation of the effect from heavy medium induced separation.Thirty-one production shifts worth of fast float/sink data and the corresponding quick ash data are used to verify the model.The results show a small error with an arithmetic average of 0.53 and an absolute average error of 1.50.This indicates that this model has high precision.The theoretical yield from the washability curves is 76.47% for the monthly comprehensive data and 81.31% using the model data.This is for a desired cleaned coal ash of 9%.The relative error between these two is 6.33%,which is small and indicates that the predicted data can be used to rapidly evaluate the separation effect of gravity separation equipment.

Floating periodic pontoons for broad bandgaps of water waves

The narrow attenuation bands of traditional marine structures have long been a challenge in mitigating water waves.In this paper,a metastructure(MS)composed of floating periodic pontoons is proposed for broadband water wave attenuation.The interaction of surface gravity waves with the MS is investigated using linear wave theory.The potential solutions of water waves by the MS with a finite array are developed by using the eigenfunction expansion matching method(EEMM),and the band structure of the MS is calculated by the transfer matrix method(TMM),in which the evanescent modes of waves are considered.The solution is verified against the existing numerical result for a special case.Based on the present solution,the association between Bragg resonance reflection and Bloch bandgaps is examined,the effects of pontoon geometry are analyzed,and the comparison between floating MS and bottom-mounted periodic structures is conducted.A computational fluid dynamics(CFD)model is further developed to assess the structures in practical fluid environments,and the floating MS presents excellent wave attenuation performance.The study presented here may provide a promising solution for protecting the coast and offshore structures.

A viscoelastic nonlinear energy sink with an electromagnetic energy harvester:Narrow-band random response

Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.

Simulation of wave scattering over a floating platform in the ocean with a coupled CFD-IBM model

A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numericalmodel in this letter.The non-hydrostatic model is used to simulate the free surface and the uneven bottom.For thesolid body modelling,the immersed boundary method(IBM)is implemented by introducing a virtual boundaryforce into the momentum equations to emulate the boundary conditions.This implementation enhances theability of the model to simulate interactions between waves and floating structures.A numerical case involvingwave interactions with a floating platform is studied to validate the numerical model.By simulating the wavepropagation,the numerical model captures the variation of the wave scattering very well,which verifies theperformance of the numerical model and the robust strategy of the IBM.

Design Methodology Research of the Floating Foundation for the Offshore MW-Rating Wind Turbine

With the rapid growth of the offshore wind industry, the innovative floating offshore wind turbine is chosen as the most feasible device to harvest the vast wind energy in deep water area. However there is no practical design guide for the floating wind turbine especially the floating foundation. In this paper, based on the investigation on the worldwide floating wind turbine and current available expertise on floating platforms accumulated in offshore O/G （oil and gas） industry, an integrated design methodology is presented according to the specialized characteristics of wind turbine, including the type selection of foundation and mooring system, design standard, design procedure, design conditions, key technologies involved. Finally a semi-submersible floating foundation is designed to support certain megawatt-rating wind turbine of Goldwind and also performance analysis and code checks are performed to validate the design. The design method of the floating foundation provided in this paper is proved feasible and can be adopted in practical engineering design.

Scattering of Water Waves by Dual Symmetric Inclined Floating Porous Barriers Using the DBEM

The scattering of normally incident water waves by two surface-piercing inclined perforated barriers in water with a uniform finite depth is investigated within the framework of linear water wave theory.Considering that thin barriers are zero-thickness,a novel numerical method involving the the coupling of the dual boundary element method(DBEM)with damping layers is applied.In order to effectively damp out the reflected waves,two damping layers,instead of pseudoboundaries are implemented near the two side boundaries of the computational domain.Thus,the modified linearized free surface boundary conditions are formulated and used for solving both the ordinary boundary integral equation as well as the hypersingular boundary integral equation for degenerate boundaries.The newly developed numerical method is validated against analytical methods using the matched eigenfunction expansion method for the special case of two vertical barriers or the inclined angle to the vertical being zero.The influence of the length of the two damping layers has been discussed.Moreover,these findings are also validated against previous results for several cases.After validation,the numerical results for the reflection coefficient,transmission coefficient and dissipation coefficient are obtained by varying the inclination angle and porosity-effect parameter.The effects of both the inclination angle and the porosity on the amplitudes of wave forces acting on both the front and rear barriers are also investigated.It is found that the effect of the inclination angle mainly shifts the location of the extremal values of the reflection and the transmission coefficients.Additionally,a moderate value of the porosity-parameter is quite effective at dissipating wave energy and mitigating the wave loads on dual barriers.

A vertical track nonlinear energy sink

Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.

Sink节点移动的无线传感网生存时间优化算法

为提高网络最大生存时间,提出Sink节点移动的无线传感网生存时间优化算法(LOAMSN)。该算法分析Sink节点移动时的流量平衡约束、最大传输速率约束、节点能耗约束等约束条件,将生存时间优化问题转化成优化模型。提出Sink节点的移动方法,即Sink节点利用节点的度值构建其移动路径,按照此路径循环移动收集数据。将Sink节点的移动认为是离散运动,Sink节点移动的生存时间优化模型分解成若干个Sink节点静止的生存时间优化模型,采用牛顿法求解每个Sink节点静止的优化模型,获得网络最大生存时间和节点发送数据量的最优值。仿真结果表明:LOAMSN算法能减少Sink节点停留位置上的节点能耗,平衡网络负载和节点能耗,提高网络最大生存时间。在一定条件下,LOAMSN算法比Sink节点静止时更优。

广义估计方程评估浮针法联合穴位埋线治疗不同分期膝骨关节炎的疗效

背景:穴位埋线法和浮针疗法是治疗膝骨关节炎的方法,但关于两种方法联合治疗的效果研究还鲜有报道。目的:运用广义估计方程探讨穴位埋线联合浮针法对不同分期膝骨关节炎的治疗效果。方法:选择2019年2月至2023年2月东莞市中医院收治的膝骨关节炎患者436例作为研究对象,随机分为2组,对照组(n=218)采用浮针法,观察组(n=218)采用穴位埋线法结合浮针疗法。以K-L分期方法为原则进行分期,其中对照组Ⅰ期57例,Ⅱ期62例,Ⅲ期49例,Ⅳ期50例;观察组Ⅰ期48例,Ⅱ期66例,Ⅲ期63例,Ⅳ期41例。比较两组患者治疗前后各指标水平及临床疗效;采用广义估计方程模型分析临床疗效的影响因素以及不同时点、不同方法、不同分期对治疗效果影响的交互效应。结果与结论:①观察组与对照组以及不同分期患者之间的基线资料均无显著差异(P>0.05),具有可比性;②两组患者经过治疗后Ⅰ期患者的治愈率最高,观察组总好转率显著高于对照组;组内比较,不同分期患者治愈率差异均有显著性意义(P<0.05);③两组患者经过治疗后各项指标均显著下降,对照组治疗4周后各指标不同分期患者相比差异均有显著性意义(P<0.05);观察组患者治疗2周后,各项指标不同分期患者相比差异即有显著性意义(P<0.05),且观察组治疗4周后各项指标均低于对照组(P<0.05),治疗效果优于对照组;④广义估计方程模型分析结果显示,创伤史、白细胞介素6水平、治疗方法、治疗时间和K-L分期均显著影响患者的临床疗效;⑤交互效应分析中,治疗2周两组患者中Ⅲ、Ⅳ期的目测类比评分有统计学意义(P<0.05);治疗4周时,两组患者中Ⅱ、Ⅲ、Ⅳ期患者的目测类比评分有统计学意义(P<0.05);⑥提示穴位埋线联合浮针法对不同分期膝骨关节炎的治疗效果优于单独浮针疗法,创伤史、白细胞介素6水平、治疗方法、治疗时间和K-L分期对患者的治疗效果有显著影响。

Seismic Response of Submerged Floating Tunnel Tether

A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.

Wave Radiation and Diffraction by A Two-Dimensional Floating Body with An Opening Near A Side Wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.

An Improved Simplified Method for Predicting the Hydroelastic Response of Mat-Like VLFS

Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient approach would obviously be the analytical one, Within the category of analytical approaches, the simplified method proposed by Ohkusu and his colleague are of special characteristics. However, when one studies their methods, several questions arise. The purpose of this paper is to critically study the simplified methods proposed by Ohkusu and his colleague in order to answer these questions. Some problems in their original methods have been found and possible improvements are suggested. It is concluded that the improved simplified method using the same idea of Ohkusu and his colleague could provide a reasonable estimate of the hydroelastic response of mat-like VLFS in a certain range of incident angles of waves.

Time Domain Simulation of Transient Responses of Very Large Floating Structures Under Unsteady External Loads

A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.

Analysis of Responses of Floating Dual Pontoon Structure

A numerical model is developed by use of the boundary integral equation method to investigate the responses of a two-dimensional floating structure. The structure under consideration consisting of two pontoons, is connected by a rigid framework, and linked to the sea floor by a mooring system. The theoretical conception is based on potential theory with hnear external forces, and applied to an arbitrarily shaped body and water depth. The discussion includes the influence of draft and space between pontoons on the responses of the floating structure. Finally, the validity of the method is adequately verified by experimental results.

Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt num- bers at the plates are discussed numerically and presented through graphs.

Structural Strength Analysis of a Tri-Floater Floating Foundation for Offshore VAWT

Vertical axis wind turbines(VAWTs) are advantageous for the development of large-scale offshore wind power because the drive system is located at the bottom of the turbine. This study investigates the structural strength of a tri-floater floating foundation supporting a 2.6 MW Darrieus VAWT. Finite element models of the floating foundation were developed using space plate-beam elements. The environmental loads, such as the aerodynamic loads, static wind loads, and wave-current loads, were considered. The general strengths of the floating foundation were calculated for the normal operating case(a cut-out wind speed of 25 m s^(-1) and blade rotation of 12 r min^(-1) were used to analyze the most unfavorable loads) and an extreme case(wind speed of 40 m s^(-1) and parked blades), and the weak components of the structure were analyzed. The results show that the floating foundation meets the strength requirements and the structural stress is highest when the wave, wind, and current are in a collinear direction. The main and secondary supporting bars transmit the loads between the stand columns and the tower foundation, and their stresses are higher than those in the other components. In the actual design, these supporting bars should be strengthened. The aerodynamic loads are very important and should be considered in the structural strength analysis of the floating foundation and the floating wind turbine system.