Two-degree-of-freedom inclined cable galloping—Part 1: General formulation and solution for perfectly tuned system

Galloping of inclined cables and other slender structures can occur in the critical Reynolds number range and/or in skew winds due to associated changes in the static force coefficients, even for cross-sections that are otherwise stable. A complete model of the quasi-steady aerodynamic forces leading to galloping has therefore been developed, for vibrations of any cylinder in two translatory degrees of freedom. It allows for arbitrary orientations of the flow velocity and the undamped vibration plane axes relative to the cylinder, and for variation of the force coefficients with Reynolds number and the relative angles. Analytical treatment of the eigenvalue problem has then led to an explicit expression for the minimum structural damping ratio required to prevent galloping for a perfectly tuned two-degree-of-freedom system, which it has been shown can differ significantly from the damping requirement for single-degree-of-freedom motion.     

Experimental study on the wind-induced vibration of a dry inclined cable—Part II: Proposed mechanisms

The possibility of dry inclined cable galloping is of concern in the design of bridge stay cables. Although the phenomenon has only been observed in a few experimental studies, the fact that the mechanism of excitation is not fully understood makes it difficult to develop solutions with confidence. To clarify its physical nature, a series of dynamic and static model wind tunnel tests have been carried out in the current study. The present paper will focus on exploring the applicability of Den Hartog criterion and on an explanation of its driving mechanism. The spatial structure of the flow field surrounding an inclined cable will be examined to assist in better understanding of the phenomenon. Results show that the critical onset condition of the divergent motion predicted by the Den Hartog criterion (as applied to an inclined circular cylinder) agrees well with the experimental observation. However, satisfaction of the criterion only occurs within a critical range of Reynolds number. Further, within the critical ranges of wind speed and cable orientation, flow around the cable is found to be better organized. The resultant fluid forces acting at different longitudinal locations of the cable tend to point toward the same direction which generates greater cross-flow excitation force, and the axis-wise lift correlation is enhanced.     

用于索承结构中斜拉索开环振动控制的磁流变阻尼器设计

斜拉索被广泛应用于索承结构,如大跨度桥梁或屋盖结构等.由于极低的内在阻尼,斜拉索易发生因其支承的运动或天气状况影响而引起的大幅值的振动.这些振动可以危及斜拉索本身以及整个索承结构的安全与寿命,甚至引起人们对该类结构信心的降低.在斜拉索减振的诸多方法中,采用磁流变阻尼器的智能阻尼技术近来引起了人们的研究兴趣.该阻尼器的阻尼特性可以通过调节(控制)磁场的输入电流/电压而改变,从而实现在不同振动(频率及幅值)情况下的最优或次优减振效果.本文发展了一个数学模型用于评价在开环控制状态下斜拉索-阻尼器系统的阻尼比.该模型考虑了阻尼器的安装高度、阻尼系数、刚度、质量、支撑刚度、磁变阻尼力以及斜拉索的垂度与倾角等因素,推导出了一个‘广义的通用公式’用于阻尼器参数的设计与优化,即寻求可提供系统最大阻尼比的最佳阻尼器参数.本文以目前世界最长斜拉桥——苏通大桥的最长斜拉索为例,确定了能够提供足够的阻尼以抑制风雨振的阻尼器安装高度以及相应的阻尼器参数.     

三维新月形变截面覆冰斜拉索气动力特性研究

为研究变截面覆冰对斜拉索气动力特性的影响,应用FLUENT中的SST k-ω 模型对三维新月形变截面覆冰斜拉索绕流场进行数值模拟;将变截面覆冰斜拉索模型划分为6个节段,分别监测不同覆冰厚度节段的气动力,得到全攻角下各节段以及全索的阻力系数和升力系数;基于Den Hartog机制,获得驰振力系数,进而研究变截面覆冰斜拉索的驰振稳定性。结果表明:变截面覆冰形态对斜拉索的流场分布影响较大,其绕流场具有明显的三维流动特性;由于覆冰厚度的变化,变截面覆冰斜拉索各节段表现出不同的气动力特性和驰振稳定性;经过三维模拟计算,变截面覆冰斜拉索各节段及全索的部分驰振力系数小于0,拉索具有发生覆冰驰振的可能性,变截面覆冰对斜拉索的气动力特性影响较大。     

缠绕螺旋线的斜拉桥斜拉索平均气动阻力特性的试验研究

通过天平测力风洞试验,在雷诺数为13×104~43×104范围内,对直径为120mm的光滑斜拉索模型和25种螺旋线斜拉索模型进行测力试验,得到了各个工况下阻力系数随雷诺数的变化规律,分析了螺旋线直径、缠绕间距对阻力系数的影响|将气动力系数按照亚临界、临界和超临界雷诺数区域进行分区,得到了各个区域内阻力系数的数值或者拟合公式|结果表明：缠绕螺旋线能减弱雷诺数效应|针对螺旋线直径相同缠绕间距不同的情况,在超临界雷诺数区阻力系数随缠绕间距的增大呈单调减小的趋势|针对缠绕间距相同螺旋线直径不同的情况,在超临界区阻力系数随螺旋线直径的增大呈单调增大的趋势|在具有抑振效果的螺旋线参数组合中,选择使得气动阻力最小的参数,可达到优化设计的目的。     

非圆截面斜拉索气动性能风洞试验研究

大跨度斜拉桥斜拉索上的风荷载对于主梁位移和内力的贡献占整个风荷载的60%~70%,斜拉索的气动力是静力和稳定性检算的基础,准确掌握斜拉索的气动力具有重要意义。通过天平测力风洞试验,在雷诺数为10×104~42×104,对直径为120mm的圆形截面斜拉索模型和3种非圆截面模型进行测力试验,得到各个工况下阻力系数随雷诺数的变化规律,分析截面变形、风向角对阻力系数的影响。结果表明：斜拉索截面变化能够增强雷诺数效应,风向角在0°~30°情况下,阻力系数随斜拉索截面变形的程度呈单调减小的趋势;风向角在40°~90°情况下,阻力系数随斜拉索截面变形的程度呈单调增大的趋势。将气动力系数和风向角度按照亚临界、临界和超临界雷诺数区域进行分区,得到各个区域内阻力系数的数值和拟合公式,通过拟合公式,可以方便地为类似截面结构的风荷载设计提供依据。     

拉索间距及覆冰对双索尾流驰振的影响

利用FLUENT中的SST模型对不同索距的扇形覆冰双索和无覆冰双索绕流场进行三维数值模拟,得到下游索在0°~90°风攻角下的阻力系数、升力系数以及驰振力系数,进而研究两索之间的距离、风攻角及有无覆冰等条件对双索尾流驰振稳定性的影响。结果表明:覆冰双索三维数值模拟结果与无覆冰双索三维数值模拟结果差异较大;覆冰双索比无覆冰双索更易发生尾流驰振失稳;拉索间距越近,发生尾流驰振的可能性更大,当覆冰拉索间距超过一定范围时,不会发生尾流驰振失稳;双索发生尾流驰振的风攻角范围与拉索之间的距离有关,拉索间距越近,发生尾流驰振失稳的风攻角越小;不同间距双索的绕流场存在很大差异,当拉索间距较近时,类似于单钝体绕流。     

缆索承重桥并列索尾流致气弹失稳研究

为了研究表面粗糙度和雷诺数对并列索尾流致气弹失稳的影响规律,以圆心间距为4D(D为圆柱直径)的双圆柱为研究对象,通过风洞试验,在风向角α=0°～20°、雷诺数Re=18000～168800,研究下游圆柱发生尾流失稳的起振条件、振动幅度及运动轨迹等振动特性,分析增大阻尼比对尾流失稳的减振效果,探讨了圆柱表面粗糙度和雷诺数对尾流失稳的作用效应。研究表明,下游圆柱在不同的风向角及风速条件下会出现尾流驰振和尾流颤振2种气弹失稳形式;增大阻尼比对尾流驰振有明显的减振效果,但对尾流颤振的影响较小。尾流致气弹失稳有明显的雷诺数效应,随着雷诺数的增大,下游圆柱的振动形式会由尾流驰振转变为尾流颤振。增加上游圆柱表面粗糙度对下游圆柱气弹失稳的影响较小;而增大下游圆柱表面粗糙度,则会明显降低下游圆柱出现尾流失稳的可能性,并会使发散性振动转变为“限幅限速”振动。     

Three-dimensional behavior of galloping in telecommunication cables of figure-8 section

It has been reported that many telecommunication cables of figure-8 section suffered from operating problems and sometimes even failed because of wind-induced large-amplitude galloping oscillation. In this study three-dimensional figure-8 cable model was tested in the wind tunnel and aeroelastic behavior of the cable was observed in detail. It is found that wind-induced change in the angle of attack of the wind relative to the cable is significant and this is the fundamental cause of galloping. The critical wind speed that triggers galloping and the initial direction of the self-excited cable motion are explained by the Den Hartog's quasi-steady treatment of the aerodynamic force with some modifications. Applicability of 3-dimensional dynamic analysis with quasi-steady wind forces was also discussed.     

猫道对大尺寸主缆气动干扰效应风洞试验研究

悬索桥施工期猫道对主缆存在气动干扰效应,从而可能对主缆的驰振性能产生一定影响。文章选取某大跨悬索桥施工期主缆尖顶型和平顶型两种施工方案中共五种工况进行研究。首先,采用3D打印技术制作主缆模型,利用风洞试验方法分别得到不考虑猫道气动干扰影响及考虑猫道气动干扰影响下五种工况的气动力系数,并进行对比分析|然后根据登哈托判据对主缆在-3°～3°风攻角范围内的驰振性能进行分析和对比。结果表明：猫道的气动干扰效应使主缆的阻力系数有所减小,升力系数也发生了明显改变|猫道对0°风攻角时主缆1#和4#驰振性能影响较大,在分析施工期主缆的驰振现象时,猫道的气动干扰效应不能忽略。     

Simple model of rain-wind-induced vibrations of stayed cables

This paper proposes a single-degree-of-freedom model of rain-wind-induced vibrations in stayed cables. It is assumed that the frequency of the circumferential motion of the upper rivulet is equal to that of cable and the rivulet amplitude is set constant for a given wind speed. The obtained results are verified with the existing experimental data showing that these assumptions capture the qualitative properties of the phenomenon. The explicit, analytical expressions are derived for the aerodynamic damping and exciting force. Finally, a linear SDOF model is derived for simple estimation of the amplitude of cable vibrations induced by wind and rain.     

斜拉桥拉索风雨激振的两质量三自由度理论模型

斜拉索的风雨激振严重地影响到斜拉索以至于斜拉桥的安全,其机理至今仍无定论。同时考虑拉索面内和面外两个自由度,并假设拉索和水线之间的作用力为库仑阻尼力和线性阻尼力,建立斜拉桥拉索风雨激振的两质量三自由度理论模型。采用Runge-Kutta法对拉索和水线的耦合方程进行数值求解,得到拉索和水线的运动规律。与仅考虑拉索面内自由度的两质量两自由度理论模型相比,考虑拉索面内面外自由度的两质量三自由度理论模型的起振风速区更多,这主要是因为拉索的水平气动力系数也存在突降,且拉索面内面外运动是相互耦合的。水线上的气动力和重力为水线提供总体的平衡;阻尼力则消耗水线的能量;至少一个方向的拉索运动引起的附加惯性力(竖向或水平)一直对水线做正功。     

Computational study on aerodynamic mitigation of wind-induced, large-amplitude vibrations of stay cables with strakes

Modifications of circular cylinder surfaces, such as strakes and helical wires, effectively mitigate Kármán vortex-induced vibrations normal to flow and have been applied to the reduction of large-amplitude vibrations of stay cables in bridges, which occur under wind oblique to a cable with or without rainfall. This aerodynamic control method cannot be fully effective without understanding the behavior of the flow around and the associated forces on oblique cables. To address this issue, flow around a yawed cylinder with various strake patterns was studied using three-dimensional detached eddy simulation (DES) at Reynolds number of 1.4×10⁵. Results demonstrated that strake patterns strongly influence the development of flow structures around a yawed cylinder and therefore the associated forces on the cylinder. The results suggest that particular strake patterns can mitigate large-amplitude and low-frequency vibrations of stay cables induced by oblique wind.     

Experimental study of wind–rain-induced cable vibration using a new model setup scheme

Wind–rain tunnel test of cable section model is one of the effective ways to explore mechanism of wind-rain-induced cable vibration and its mitigation. However, most of previous model setup schemes consider vertical vibration of cable only, in which the restoring force comes from the springs that perpendicularly support the cable model at its two ends. In this short communication, a new setup scheme for experimental study of wind–rain-induced cable vibration is presented. It can simulate both horizontal and vertical vibrations of the cable, in which the restoring force of the cable model comes from cable tension forces as in the prototype cable. Furthermore, the new setup can be easily adjusted for different cable inclinations and yaw angles. The frequency equation of the cable model is first derived to facilitate the design of model setup. Vortex-induced cable vibration, galloping of cable with artificial rivulet and wind–rain-induced cable vibration are then reproduced in wind/wind–rain tunnel using the new setup scheme. The preliminary parameter study, including cable inclination, yaw angle, and rainfall, regarding wind–rain-induced cable vibration is also performed. The effectiveness of vibration control methods, such as increasing damping ratio and twining spiral wire on the cable surface, is finally investigated.     

Thin water film around a cable subject to wind

Cables of cable-stayed bridges can experience rain–wind-induced vibrations (RWIV). This instability involves lower frequencies and higher amplitudes than classical vortex-induced vibrations. Furthermore, RWIV is restricted to a certain range of wind velocities, unlike linear 1 dof galloping. When flowing along the cables, the water gathers near the separation points to form one or two rivulets. Former studies which have described the coupling between the rivulets’ motion and the cable motion assume the existence of at least one rivulet. In this paper, we address the conditions for the formation of the rivulets. A two-dimensional model is developed within the lubrication theory, describing the evolution of a thin film subjected to gravity, surface tension, wind and motion of the cylinder. Numerical simulations show the appearance of the rivulets that are reputedly responsible for the instability. The position at which the rivulets appear is found to vary with the wind speed and the predictions of the model are in good agreement with new experimental data.     

A wind tunnel study on control methods for cable dry-galloping

The common vibration of cable caused by rain-wind combination has been known as most typical type and a lot kind of its countermeasures has been proposed for suppressing this phenomenon. Recently, stayed-cables were also proved that they could be excited in dry state (without rain), which is called dry-galloping. Recently, its mechanisms have been explained by axial flow, Reynolds number and so on. To clarify the characteristics of this galloping, wind tunnel test of a cable model with various kinds of wind angle was conducted. Then, three types of countermeasure were examined to suppress dry- galloping of bridge cable. The tests confirmed that the occurrence of dry-galloping depends on relative wind attacked angles and onset reduced wind speed. Furthermore, single spiral wire, double spiral wire and circular ring were found to have high effectiveness in mitigating this galloping when those are installed properly.     

Regen‐Wind‐induzierte Schwingungen – ein State‐of‐the‐Art Report

Rain‐wind induced vibrations can occur, when rain and wind simultaneously act, for instance, on the cables of cable‐stayed bridges, on inclined steel hangers of arch bridges or on the backstays of guyed masts. As a result of wind and gravity, the rainwater forms small rivulets, which flow down on the surface of these structural members. The rivulets disturb the wind flow around the dry cross section and cause a modified unsymmetrical distribution of the surrounding wind pressure, which leads to periodic exciting forces. Due to the movement of the cable and the wind forces, the position of the rivulets varies on the cable surface. This constellation can lead to aeroelastic excitation with large amplitudes. Rain‐wind induced vibrations can reduce the life cycle of a structure seriously, because the initialising wind velocity of rain‐wind induced vibrations is significantly lower than the design wind velocity and thus has a high probability of occurrence. In this paper, the further researches and investigations up to now dealing with rain‐wind induced vibrations are summed and commented.     

Buckling analysis of a cable-stayed circular frame

Large parabolic dish concentrators have been widely employed in solar thermal applications. The supporting structure of a solar dish concentrator consists of a circular frame, a central post, and front and rear cables connecting the frame to the post. The tensions in the cables cause compressive stresses in the circular frame and the central post, and this support structure must be designed for stability. In this paper, the nonlinear buckling behavior of the supporting structure of a cable-stayed circular frame is studied in detail. A three-dimensional finite element model of the supporting structure is developed to predict the critical cable tensions that would cause buckling of the circular frame and to determine the associated buckling mode shapes of the supporting structural system. The results show that the buckling load of a cable-stayed circular frame depends not only upon the cross-section of the frame, but also upon the number of cables and the inclinations of the cables. In all cases, in-plane buckling modes are predominant. The concentrated torques resulting from unbalanced cable tensions tend to induce the out-of-plane buckling modes.     

Characterization of flow oblique to a circular cylinder with low aspect ratio using 3-D detached eddy simulation

Large-amplitude vibrations of stay cables in cable-stayed bridges can threaten the safety and serviceability of the structures. Understanding of the excitation mechanism is necessary to mitigate such vibrations effectively and efficiently. Experimental research has investigated the mechanism of oscillation using flow oblique to a cylinder; however, since the aspect ratio of the cylinder is much lower than that of a real stay cable in bridges, the results might not reliably describe the real phenomenon. The aim of this study is (1) to provide better understanding of aspect ratio effects of a circular cylinder on aerodynamic characteristics of the cylinder oblique to flow associated with the large-amplitude cable vibrations and (2) to provide the experimentalists suggestions of a requisite aspect ratio and appropriate pressure-measuring positions of a cylinder for fully developed flow around the cylinder. To this end, the current work applied three-dimensional detached eddy simulations (DES) to flow around a yawed and inclined cylinder to investigate the importance of the aspect ratio of the cylinder when flow oblique to the cylinder develops fully along its spanwise axis. The Reynolds number is 1.4 × 10⁵ based on the incoming flow velocity and the diameter of the cylinder. Three aspect ratios (L/D=10, 20, and 30; L: a cylinder length; D: a cylinder diameter) and two numerical conditions (slip and periodic) on spanwise boundaries were employed. Results showed that three-dimensional flow and the associated forces on a yawed and inclined cylinder are significantly influenced by the spanwise aspect ratios and spanwise boundary conditions. This study suggests that when a wind tunnel experiment investigates flow oblique to a very slender cylinder, such as attempting to model a stay cable, experimentalists should use a sufficiently high spanwise aspect ratio of the cylinder. For the case of the 30° yaw and 45° inclined cylinder, the requisite ratio would be approximately 60 or higher and appropriate pressure-measuring positions of a half to two-thirds of the cylinder length from its upper/upstream end in order to accurately model inherently three-dimensional characteristics of the flow.     

Dry galloping characteristics and its mechanism of inclined/yawed cables

Mechanism of dry galloping of inclined cable of cable-stayed bridges is described in relation to Karman vortex mitigation. Furthermore, the role of Scruton number Sc on reduced critical velocity Vrcr of the dry galloping is investigated for practical use basing on wind tunnel tests and field observations of dry galloping or pseudo-galloping, which is classified as cable vibration with rain-state but response amplitude is abnormally large. It is verified that as far as the divergent-type of dry galloping, the design criterion subject to Sc-Vrcr proposed by FHWA (Federal Highway Administration of U.S.) seems to be reasonable for practical use, on the other hand, for the unsteady dry galloping, the Saito criterion for Sc-Vrcr diagram seems to be reasonable.