Random vortex induced vibration response of suspended flexible cable to fluctuating wind

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled equations.The first equation is a partial differential equation governing the cable vibration.The second equation is a wake oscillator that models the lift coefficient acting on the cable.The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic one.In the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration.In the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind.Using the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration system.Depending on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration.By applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted.Then,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations.Some numerical simulation results confirm the obtained analytical results.It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration.Thus,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

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.

Vibration Response and Stress Analysis of Planar Elastic Tube Bundle Induced by Fluid Flow

Flow?induced vibration plays a positive role on heat transfer enhancement. Meanwhile, it is also a negative factor for fatigue strength. Satisfying the fatigue strength is the primary prerequisite for heat transfer enhancement. This paper numerically studied the flow?induced vibration of planar elastic tube bundle based on a two?way fluid–structure interaction(FSI) calculation. The numerical calculation involved the unsteady, three?dimensional incompressible governing equations solved with finite volume approach and the dynamic balance equation of planar elastic tube bundle solved with finite element method combined with dynamic mesh scheme. The numerical approach was verified by comparing with the published experimental results. Then the vibration trajectory, deformation and stress contour of planar elastic tube bundle were all studied. Results show that the combined movement of planar elastic tube bundle represents the agitation from inside to outside. The vibration of out?of?plane is the main vibration form with the typically sinusoidal behavior because the magnitude of displacement along the out?of?plane direction is the 100 times than the value of in?plane direction. The dangerous point locates in the innermost tube where the equivalent stress can be utilized to study the multiaxial fatigue of planar elastic tube bundle due to the alternating stress concentration. In the velocity range of 0.2-3 m/s, it is inferred that the vibration amplitude plays a role on the stress response and the stress amplitude is susceptible to the fluid velocity. This research paves a way for studying the fatigue strength of planar elastic tube bundle by flow?induced vibration.

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.

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.

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.

Vibration Control Induced by Ice of a Jacket Platform

Based on the self-excited vibration theory of ice, the vibration control technology of jacket platform is studied in this paper. The magnetorheological suspensions (MR) unit is chosen as the damper, the control objective function for vibration excited by ice is determined by instantaneous optimal control (IOC) method, and genetic algorithm (GA) is used to select the optimal control force. For the jacket platform of 40 m in height and a 3-floor deck, the vibration responses induced by ice have been calculated before and after control considering the different thickness and speed of ice. It is shown that the control method presented in this paper can reduce the vibration response by 30%, and it is feasible to adopt MR absorber and GA in the control of vibration induced by ice.

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.

Wind-induced vibration of single-layer reticulated shell structures

Aiming at the dynamic response of reticulated shell structures under wind load,systematic parameter analyses on wind-induced responses of Kiewitt6-6 type single-layer spherical reticulated shell structures and three-way grid single-layer cylindrical reticulated shell structures were performed with the random simulation method in time domain,including geometric parameters,structural parameters and aerodynamic parameters.Moreover,a wind-induced vibration coefficient was obtained,which can be a reference to the wind-resistance design of reticulated shell structures.The results indicate that the geometric parameters are the most important factor influencing wind-induced responses of the reticulated shell structures;the wind-induced vibration coeffi-cient is 3.0-3.2 for the spherical reticulated shell structures and that is 2.8-3.0 for the cylindrical reticula-ted shell structures,which shows that the wind-induced vibration coefficients of these two kinds of space frames are well-proportioned.

Effects of Span Length and Additional Structure on Flow-Induced Transverse Vibration Characteristic of a Cantilevered Rectangular Prism

We consider the effects of the aspect ratio L/H (where L is the length of a prism, and H is the height of a prism normal to the flow direction) and the size of additional structures (which are a plate and a fin on the surface of a prism) on a vibration characteristic of a cantilevered rectangular prism. The present research is intended to support the analysis of energy harvesting research on the flow-induced vibration in water flow using a magnetostrictive phenomenon. The prisms are constructed from stainless steel and mounted elastically to a plate spring attached to the ceiling wall of the water tunnel. The prisms with aspect ratios of L/H ≥ 5 have reasonably identical vibration characteristics. However, the difference in the vibration characteristic appears distinctly on a rectangular prism with an aspect ratio of L/H = 2.5. The rectangular prism with an aspect ratio of L/H = 10 and a side ratio of D/H = 0.2 has a stable and large response amplitude and oscillates with a lower velocity. The length of the added plate and the size of the added fin influence the velocity of vibration onset. If the length of the added plate and fin size on the rectangular prism with D/H = 0.2 becomes large, the curve of the response amplitude shifts to that of the rectangular prism with D/H= 0.5. The response amplitude of the rectangular prism with/without plate or fin is found to be related to the second moment of area of the prism.

Wind-induced responses of super-large cooling towers

Traditional gust load factor(GLF)method,inertial wind load(IWL)method and tri-component method(LRC+IWL)cannot accurately analyze the wind-induced responses of super-large cooling towers,so the real combination formulas of fluctuating wind-induced responses and equivalent static wind loads(ESWLSs)were derived based on structural dynamics and random vibration theory.The consistent coupled method(CCM)was presented to compensate the coupled term between background and resonant response.Taking the super-large cooling tower(H=215 m)of nuclear power plant in Jiangxi Province,China,which is the highest and largest in China,as the example,based on modified equivalent beam-net design method,the aero-elastic model for simultaneous pressure and vibration measurement of super-large cooling tower is firstly carried out.Then,combining wind tunnel test and CCM,the effects of self-excited force on the surface pressures and wind-induced responses are discussed,and the wind-induced response characteristics of background component,resonant component,coupled term between background and resonant response,fluctuating responses,and wind vibration coefficients are discussed.It can be concluded that wind-induced response mechanism must be understood to direct the wind resistant design for super-large cooling towers.

Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings

Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance(me) vibration is induced and could lead to sub?synchronous vibration accidents for high?speed turbocharger(TC). There are very few research works that focus on the magnitude e ects on such induced unbalance vibration. In this paper, a finite element model(FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings(FRBs). The nonlinear dynamic responses of the TC rotor system with di erent levels of induced unbalance magni?tude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub?synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear e ects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 gbration 1·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vi×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un?balance magnitude of turbine wheel and compressor wheel for the high?speed TC rotor with FRBs is proposed: the value of induced un?balance magnitude should be kept around 0.2 g·mm.

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.

Investigation of Hydroelastic Ship Responses of An ULOC in Head Seas

Investigation of hydroelastic ship responses has been brought to the attention of the scientific and engineering world for several decades. There are two kinds of high-frequency vibrations in general ship responses to a large ocean-going ship in its shipping line, so-called springing and whipping, which are important for the determination of design wave load and fatigue damage as well. Because of the huge scale of an ultra large ore cartier （ULOC）, it will suffer seldom slamming events in the ocean. The resonance vibration with high frequency is springing, which is caused by continuous wave excitation. In this paper, the wave-induced vibrations of the ULOC are addressed by experimental and numerical methods according to 2D and 3D hydroelasticity theories and an elastic model under full-load and ballast conditions. The influence of loading conditions on high-frequency vibration is studied both by numerical and experimental results. Wave-induced vibrations are higher under ballast condition including the wave frequency part, the multiple frequencies part, the 2-node and the 3-node vertical bending parts of the hydroelastic responses. The predicted results from the 2D method have less accuracy than the 3D method especially under ballast condition because of the slender-body assumption in the former method. The applicability of the 2D method and the further development of nonlinear effects to 3D method in the prediction of hydroelastic responses of the ULOC are discussed.

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.

Numerical Calculation Methods for Wavemaking Response Induced by Explosion in Harbour

Using the axial symmetry results of marker and cell (MAC) method as initial value in this paper, two numerical calculating methods are presented for the late wavemaking response induced by explosion in harbour. One of the methods is the superposition method of the vibration mode based on fluid slosh in container. Another one is the joining method of the MAC results with the shallow wave theory calculation in time domain. As a practical example, it is conducted to the numerical calculation about 1000 ton TNT equivalent explosion within touch of water surface. The results show that it can be rationally described with the methods to the wavemaking progress and character. The numerical results are identical with the observed scene on the spot experiment. The methods are simple and applicable in the engineering design.

Effect of Mass Ratio on Hydrodynamic Response of a Flexible Cylinder

灵活圆形的柱体的导致流动的颤动(FIV ) 上的集体比率的效果试验性地在一辆拖引的坦克被调查。分别地，有 7.9 公里和 4.8 公里的外部、内部的直径的一个 Tygon 试管为学习被采用。试管被连接到一辆马车并且从休息拖引到一稳定在慢下来在 1.6 m 的距离上再休息在前加快 m/s 到 1.6 仍然流水。雷纳兹数字基于柱体，外部直径是 80013,000，并且减少的速度(柱体天赋频率使正常化的速度和外部直径) 从 2 ～ 25 跨越了。当连接时，柱体在 11 N 的轴的虚荣下面从 420 公里被伸长到 460 公里。把伸长的长度基于柱体，方面比率(到外部直径的柱体长度的比率) 作为 58 被计算。三集体比率(柱体的比率结构的质量到代替的液体质量， m *) 被分别地用空气，水，和合金粉末(nickel-chromium-boron 矩阵合金) 填满柱体内部 0.7， 1.0，和 3.4 决定。一个光方法为反应大小被采用。多频率颤动在两个被观察同轴(IL ) 并且跨流动(CF ) 回答；在高级雷纳兹数字，颤动模式直到 3 rd 在 CF 反应被识别。模式转变被发现为最高测试的集体比率在更低的减少的速度发生。颤动振幅和频率关于减少的速度被确定并且表示。一个重要减少的颤动振幅与增加集体比率在 IL 反应被发现，并且仅仅起始、上面的分支在 IL 和 CF 反应振幅存在。规范的反应频率被揭示线性地关于减少的速度增加，并且为线性关系的斜坡被发现为测试的三格相同。

A study of ice response spectra

Some problems concerning the ice forces and ice response spectra are studied from both theoretical and practical points of view. On the basis of structural analysis,the analysis method of ice response spectra is proposed, since it plays an important role in the prediction of maximum structural response in cold regions. And it is illustrated that it is easy to study the structural response to ice using the ice response spectra.

A More Precise Computation of Along Wind Dynamic Response Analysis for Tall Buildings Built in Urban Areas

Modern tall buildings are generally built in urban areas, where value of the terrain roughness length is much greater than that of the general terrain areas, therefore wind-induced vibrations become more pronounced. The present formulas of numerical analysis of wind-induced response become less accurate. A more accurate expression of along-wind load spectrum matrix is proposed. On the basis of the expression, structural analysis formula of along-wind displacement and acceleration response are developed and programmed. The rationality of these formulas are illustrated in examples.

胶囊形气膜结构风致气弹响应及风振系数研究

针对1/3矢跨比胶囊形气膜结构进行了气弹模型风洞试验,研究了结构的风致气弹响应变化规律,并给出了可供设计参考的风振系数。研究发现:结构平均变形呈迎风面凹陷,顶部隆起,横风向向外凸出的趋势,且这种变形趋势随着内压减小和风速增大越来越明显。0°风向角时的平均变形和振幅大于45°风向角时的平均变形和振幅大于90°风向角时的平均变形和振幅,结构合位移均值的极值出现在迎风面与顶面中心点;0°和45°风向角下,顶点竖向振幅>顺风向振幅>横风向振幅,结构以1阶模态振动为主;90°风向角下,顶点横风向振幅大于其他两个方向,结构以1阶和2阶模态叠加振动为主。各工况下结构的内压均有不同程度的减小。最后给出了考虑流固耦合效应的响应风振系数。