Dynamic Response of Two-Degree-of-Freedom Riserless Drill String for Vortex-Induced Vibration Suppression and Enhancement

The mechanical behavior,dynamic evolution,and flow-field distribution of a two-degree-of-freedom riserless drill string were simulated numerically by using FLUENT fluid simulation software with the user-defined function embedded.The rotation angular velocities before and after the critical rotation angular velocity were used as independent variables,and the reduced velocity range was 3-14.Fluid-structure coupling was realized based on the dynamic overset grid and the SST k-ωturbulence model.Results reveal that the dynamic response of the riserless drill string was considerably affected by rotation and flow velocity,which are coupled with each other.The cross-flow average dimensionless displacement increased with the rotation angular velocity,and rotation considerably enhanced the in-line maximum average dimensionless displacement.However,the cross-flow amplitude caused by vortex-induced vibration was suppressed when the rotation angular velocity reached a certain value.The in-line and cross-flow frequencies were the same,thereby causing the trajectory to deviate from the standard'figure-eight'shape and become a closed circle shape.The vortex did not fall behind the cylinder at low reduced velocity with high-rotation angular velocity,and the structure of the near-wake vortex remained U-shaped.The wake of the cylinder was deflected along the cross-flow direction,thereby leading to vibration asymmetry and resulting in increased vibration instability and disordered vibration trajectories,especially at high-rotation angular velocities.

The Effect of Internal Fluid on the Response of Vortex-Induced Vibration of Marine Risers

Based on Iwan′s wake oscillator model developed with the classical van der Pol equation, the differential equation for the response of the vortex-induced vibration (VIV) of the riser considering the effect of the internal flowing fluid and the external marine environmental condition is derived. The effect of the internal flowing fluid on the response of VIV of the riser is studied by means of the Finite Element Method. The results show that the effect of the internal fluid velocity on the VIV of the riser is strong when the natural frequency of the riser is close to the vortex shedding frequency. In addition, the increase of the top tension can decrease the sensitivity of the riser to the internal fluid velocity.

Experimental Investigation of Multi-Mode Vortex-Induced Vibration of Flexible Risers with Different Mass Ratios

Experiments were conducted on risers with different mass ratios to study the effect of mode conversion and spanwise correlation. The slenderness ratio of the riser model was set as 169, and the Reynolds numbers are 1600-14400. The dynamic responses of riser models versus reduced velocity were analyzed, and the spanwise displacement, frequency,and trajectory of the mode conversion from the lower to the higher mode were explored. The results revealed that the riser model with a higher mass ratio excites a higher number of modes. The conversion region of multi-mode competition exists and narrows with the increasing mass ratio. Mode conversion is continuous and manifests as the transmission of peaks and troughs in mode shape: the peaks and troughs of mode shape move up in the mode stable development region and move down in the mode conversion region. The single-mode dominating vibration exhibits a standing wave feature, and the traveling wave feature is significant in the mode conversion region. Furthermore, the frequency jump is always transmitted from the trough to the peak of the mode shape, and finally, all the axial positions vibrate at the same frequency. The trajectory in the mode conversion region deviates from the 8-shape and recovers the standard8-shape at the middle and late stages of the mode stable development region.

Numerical Prediction of Vortex-Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration （VIV） of top tensioned riser （Till）, the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti＇ s wake oscillator model. Then Galerkin＇ s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and file corresponding numerical programs are compiled which solve the coupled equations directly in the time domain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7 is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers. The effect of internal flow on the dynamic characteristics and dynmnic response of the riser is analyzed and several valuable conelusions are drawn.

Effects of Internal Flow on Vortex-Induced Vibration and Fatigue Life of Submarine Pipelines

With the rapid development of the offshore oil industries, submarine oil / gas pipelines have been widely used. Under the complicated submarine environmental conditions, the dynamic characteristics of pipelines show some new features due to the existence of both internal and external flows. The paper is intended to investigate the vortex-induced vibration of the suspended pipeline span exposed to submarine steady flow. Especially, the effects of the flow inside the pipeline are taken into account. Its influences on the amplitude of pipeline response, and then on the fatigue life, are given in terms of the velocity of the internal flow.

Experimental Study on Vortex-Induced Vibration Coupling Wake Interference of Multi-Riser Groups with Sensitive Spacing

The“riser group−fluid between risers”is taken as the carrier,and the experiment on vortex-induced vibration of tandem riser groups coupling interference effect under sensitive spacing is performed.The least-square method is used to linearly fit the reduced velocity and main frequency,and the rule of Strouhal numbers is analyzed.Each mode is separated based on the mode decomposition theory,and the mode conversion mechanism is also explored.The concept of“interference efficiency”is introduced to study the dynamic characteristics and response evolutions of different riser groups.The results show that the wake shielding effect widely exists in tandem riser groups,and the interference effect of midstream and downstream risers on their upstream risers is significantly lower than that of upstream risers on midstream and downstream risers.The trajectories of midstream and downstream risers lag behind their upstream risers due to multiple shadowing effects,the vibration frequency range of downstream riser is widened and the dominant frequency is extremely unstable.Compared with the isolated riser,wake interference suppresses the vibration dis-placement of the midstream and downstream risers in the in-line direction,and enhances the displacement of upstream and midstream risers in the cross-flow direction.The interference effect of the fluid between risers at low velocities is stronger than that at higher velocities,and the cross-flow displacements of upstream risers are always in the interference enhancement region.It is urgent to pay attention to the cross-flow displacement of upstream and midstream risers in tandem riser groups considering the safety design.

Vortex-induced vibration of pipes conveying fluid using the method of multiple scales

The nonlinear dynamics of supported pipes conveying fluid subjected to vortex-induced vibration is evaluated using the method of multiple scales. Frequency response portraits for different internal fluid velocities under lock-in conditions are obtained and the stability of steady-state responses is discussed. Results show that the internal fluid velocity has a prominent effect on the oscillation amplitude and that the steady-state responses incorporating unstable solutions in the lock-in region are also obtained. In addition, the effects of two kinds of fluctuating lift coefficients on the steady-state responses are compared with each other.

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”.

Prediction Model for Vortex-Induced Vibration of Circular Cylinder with Data of Forced Vibration

A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions （VIV） of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson＇ s group are in rather good agreement.

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration（VIV） for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line（IL） response is as important as the cross-flow（CF） response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.

An experimental investigation of dual-resonant and non-resonant responses for vortex-induced vibration of a long slender cylinder

Experimental results of the dual-resonant and non-resonant responses are presented for vortex-induced vibrations(VIV)of a long slender cylinder.The cylinder has a diameter of 10mm and a length of 3.31 m,giving an aspect ratio of 331.The cylinder was towed by a carriage with the velocity up to 1.5 m/s,with the Reynolds number varying from 2500 to 38000.Three different weights were used to provide the initial tension.Dual resonance means that resonance occurs simultaneously in both the cross-flow(CF)and in-line(IL)directions.The experiments were conducted in two stages.At the first stage,dual-resonant dynamic features of the cylinder subjected to vortex-induced excitation were investigated.The features of CF and IL vibration amplitude,motion orbits,phase angle differences,dominant frequencies and mode order numbers are presented.At the second stage of the experiments,particular emphasis was placed on non-resonant dynamic features.The variation of multi-mode modal displacement amplitudes was investigated in detail.

Identification of hydrodynamic coefficients from experiment of vortex-induced vibration of slender riser model

One of the challenges in predicting the dynamic response of deepwater risers under vortex-induced vibration （VIV） is that it runs short of believable fluid loading model. Moreover, the hydrodynamic loading is also difficult to be measured directly in the VIV experiments without disturbing the fluid field. In the present work, by means of a finite element analysis method based on the experimental data of the response displacements, the total instantaneous distributions of hydrodynamic forces together with the hydrodynamic coefficients on the riser model with large aspect ratio （length/ddiameter） of 1750 are achieved. The steady current speeds considered in the experiments of this work are ranging from 0.15 rn/s to 0.60 m/s, giving the Reynolds Number between 2400 and 9600. The hydrodynamic coefficients are evaluated at the fundamental frequency and in the higher order frequency components for both in-line and cross-flow directions. It is found that the Root-Mean Squared hydrodynamic forces of the higher order response frequency are larger than those of the fundamental response frequency. Negative lift or drag coefficients are found in the numerical results which is equivalent to the effect of fluid damping.

VIV analysis of pipelines under complex span conditions

Spans occur when a pipeline is laid on a rough undulating seabed or when upheaval buckling occurs due to constrained thermal expansion. This not only results in static and dynamic loads on the flowline at span sections,but also generates vortex induced vibration (VIV),which can lead to fatigue issues. The phenomenon,if not predicted and controlled properly,will negatively affect pipeline integrity,leading to expensive remediation and intervention work. Span analysis can be complicated by:long span lengths,a large number of spans caused by a rough seabed,and multi-span interactions. In addition,the complexity can be more onerous and challenging when soil uncertainty,concrete degradation and unknown residual lay tension are considered in the analysis. This paper describes the latest developments and a'state-of-the-art' finite element analysis program that has been developed to simulate the span response of a flowline under complex boundary and loading conditions. Both VIV and direct wave loading are captured in the analysis and the results are sequentially used for the ultimate limit state (ULS) check and fatigue life calculation.

2(3PUS+S)型并联机构驱动部件振动响应特性分析

以一种2(3PUS+S)型并联机构模拟人工髋关节摩擦磨损试验为背景,针对目前机构驱动部件振动响应特性分析需要大量理论公式推导的问题,提出了一种驱动部件振动响应特性分析的方法。使用Solid Works对驱动部件的主体部分滚珠丝杠副进行三维建模,将模型导入Adams软件中,进行动力学分析,得到单个滚珠的撞击力曲线图;然后利用Workbench进行模态分析得到系统的固有频率和振型;最后,基于瞬态动力学理论,利用Workbench软件结合滚珠和滚道的撞击力以及系统的固有频率和振型,进行振动响应分析,得到了螺母的加速度振动响应曲线。结果表明:螺母加速度振动响应的振幅和测点位置有关。通过振动响应的分析,可以验证设备可靠性,为结构参数优化设计提供理论依据。

Euler-Bernoulli海洋立管涡致强迫振动响应研究

针对海洋立管(Pipe-in-pipe,PIP)系统在海水作用下发生的振动问题,开展了对PIP系统在涡致强迫振动下的动力学响应研究,分析了在涡致强迫振动下海洋立管外管直径、轴向拉力、外激力频率对海洋立管位移响应的影响规律。基于Euler-Bernoulli双梁模型,采用Lamb-Oseen涡模型,建立了动力学模型,利用格林函数法求得该强迫振动的稳态响应。结果表明,随着管道直径增加,外激力增加,产生最大力幅值的位置离管道越远;轴向拉力对外部管道的影响较大,对内部管道的影响较小;无因次频率取0.4时,外部管道位移超出允许变形极限,内外管壁发生周期碰撞,易对海洋立管造成损伤。

两端支承式输流管路的强迫振动分析

研究水平放置的两端支承式输流管路的强迫振动问题,将欧拉-伯努利梁模型视为管路的简化力学模型.利用格林函数法对无量纲的强迫振动微分方程进行推导,得到一般支承形式管路的格林函数,并最终得到挠度的一般表达式.在此基础上研究一端固定、另一端弹性支承输流管路的振动响应,分别利用微分变换法和伽辽金法验证其正确性与准确性,并研究了集中载荷和分布载荷情况下的振动响应.利用该方法可以得到封闭的精确解,比其他数值方法具有较大的优势.

文克尔地基上矩形薄板的振动

建立文克尔地基上矩形薄板自由振动和强迫振动的微分方程并求得其通解，给出振型函数的表达式及常见支承条件下板的频率方程．

文克尔地基上阶梯式单向矩形薄板的振动

用奇异函数建立文克尔地基上阶梯式单向矩形薄板自由振动和强迫振动的微分方程并求得其通解，用Ｗ算子给出主振型函数的表达式及常见支承条件下板的频率方程，用广义函数讨论板在不同形式载荷作用下的强迫振动响应·

土-结构动力相互作用下网架结构简化分析方法研究

根据不同学者有关地基动力阻抗的计算公式,结合整体有限元法,从工程应用出发对S-R(Swing-Rocking)模型进行修正,提出适用于分析土-结构动力相互作用下大跨空间结构的简化计算方法。基于修正的S-R模型建立土-网架结构动力相互作用的计算模型,与已验证的三维整体有限元(3-D)模型进行对比分析。研究表明,根据修正S-R模型计算所得土-网架结构相互作用体系的自振特性和地震响应与已验证的3-D模型结果呈现出完全一致的规律性且吻合较好,从而验证了修正S-R模型的合理性;在不同地震波作用下,采用Gazetas提出的地基动力阻抗公式建立的土-网架结构相互作用体系中网架节点最大位移和峰值加速度与已验证的3-D模型结果最大误差不超过8.0%,结构杆件内力最大误差不超过10%,表明Gazetas提出的地基动力阻抗公式更适用于分析土-大跨空间结构动力相互作用问题,且具有较好的精度。