Wind-induced Cable Vibrations Research Articles

Monitoring-based identification of nonlinear aerodynamic damping in multi-mode vortex-induced vibrations of a stay cable

New issues of wind-induced cable vibration, i.e., multi-mode vibrations, increasingly occur in long-span bridges, which are closely associated with underlying damping features. In this study, an analytical method is proposed to identify nonlinear aerodynamic damping in multi-mode wind-induced cable vibrations in fields, involving the assessment of total and mechanical damping. The method is available to extract a series of mono-component resonances/decays from the measured signals based on the analytical mode decomposition (AMD) and random decrement technique (RDT), and then to determine the damping parameters using the Hilbert transform (HT) combined with the smoothing spline or linear least-square fitting. Furthermore, this method is applied to address the vortex-induced vibrations (VIV) of an ultra-long stay cable on the Sutong Bridge. Firstly, the vibrations are reported in terms of a typical event and one-year statistics. Subsequently, the damping parameters are identified to illustrate the in-situ aeroelasticity. The results show that the cable exhibits high-frequency vibrations primarily in the 41st to 43rd modes, and the aerodynamic damping exhibits significant amplitude-dependent nonlinearity. Finally, the damping identifications are employed to reveal the onset mechanism for the vibrations, and a Scruton number (Sc) criterion, i.e., Sc > 5.4, is suggested for mitigating the vibrations.

Role of dynamic water rivulets in the excitation of rain–wind-induced cable vibration: A critical review

It has been more than 30 years since Hikami Y and Shiraishi N (1988) Rain–wind-induced vibrations of cable-stayed bridges. Journal of Wind Engineering and Industrial Aerodynamics 29: 409–418 first reported the rain–wind-induced vibration (RWIV) of stay cables in the construction stage of Meikonishi Bridge, Japan. After that, considerable research efforts have been devoted to understanding the RWIV of stay cables, and the role of the upper rivulet has been gradually realized and studied. This study presents a selective review on recent progress of RWIV and its controversial excitation mechanism. The available knowledge and up-to-date understanding of this complex fluid-structure interaction are presented in some detail. The formation, dynamics of water rivulet, and its role in affecting the near-wall boundary layer properties and in the excitation scenario of RWIV are of particular interest in this study. Finally, some limitations of previous studies are concluded, with some perspective suggestions for further study of excitation mechanism of RWIV.

Wind-induced vibration of structural cables

The wind-induced vibration of cables has been widely studied over the past decades because of cables’ many applications in cable-stayed, suspension, and tied-arched bridges, and power transmission lines. They have been mostly investigated through research conducted on rigid model cables with a finite length and circular cross-sectional geometry that represents a section model of a long cable. These models have been considered accurate because the behavior of flow over a cable and circular cylinder is similar, although there are structural differences between them. Cables usually experience small- to large-amplitude vibration due to wind loads that causes fatigue failure and poses a significant threat to the safety and serviceability of these structures. Although this paper mainly focuses on reviewing the past studies about different types of wind-induced cable vibration, some general information related to circular cylinders has been briefly reported for better understanding of the flow over cables. This paper incorporates an extensive review based on the existing papers about different sources of wind-induced cable vibration consisting of vortex-induced vibration, rain-wind-induced vibration, dry galloping, ice galloping, and wake galloping. Furthermore, this paper explains the mechanism, vibration source, and a mitigation solution for each type based on the past studies using wind tunnel experiments, computational fluid dynamics, field measurements, or analytical approaches. This review helps to better understand the aerodynamics and fluid–structure interactions of cables with or without ice/rain on the surface, while static and dynamic wind loads act on the structure.

Application of a three-dimensional aeroelastic model to study the wind-induced response of bridge stay cables in unsteady wind conditions

The possibility of bridge stay cables experiencing violent dry inclined cable galloping raises great concern in the engineering community. Numerous experimental and analytical studies have been conducted to investigate this phenomenon, most of which were in the context of steady wind past a rigid cylindrical body. Real stay cables however, are generally long and flexible. They are exposed to more “broad” range of atmospheric boundary layer type of wind velocity profile which is also unsteady and turbulent by nature. To better understand the physics underlying this type of wind-induced cable vibration and to elucidate various contributing factors, a more realistic analytical model which is capable of addressing the above elements is imperative. In the current paper, a three-dimensional aeroelastic model is proposed to study the aerodynamic response of an inclined and/or yawed slender flexible cylindrical body subjected to unsteady mean wind, with practical application to wind-induced vibrations of bridge stay cables under no precipitation condition. The non-linear aerodynamic forces derived in the present study are combined with the cable free vibration equations available in literature to obtain the equations of motion for the wind-induced vibration of stay cables, which are solved numerically by an explicit finite difference scheme. The proposed three-dimensional aeroelastic model and numerical solution technique are validated by comparing the predicted cable free vibration responses with existing data in the literature. The mechanism which triggers dry inclined cable galloping and the required conditions for its growth are explored. In addition, the impact of different initial conditions and various unsteady mean wind scenarios on this violent cable motion are investigated. Results show that the occurrence of dry inclined cable galloping is associated with an opposite-phase relation between the relative wind speed and the aerodynamic force along the direction of cable motion in the critical flow regime. The cable would respond most violently should it be exposed to uniformly distributed steady wind in the critical Reynolds number range for a sufficiently long duration. The presence of multi-mode oscillation in a cable prior to its exposure to the critical flow condition would lead to a considerable reduction in cable response. Furthermore, the boundary layer type velocity profile would have a sizable impact on the cable aerodynamic response provided only a portion of the cable is subjected to the critical flow condition, and the unsteadiness in wind is found to have a stabilizing effect on cable aerodynamic response.

Study on the role of rivulet in rain–wind-induced cable vibration through wind tunnel testing

Rain–wind-induced vibration (RWIV) of stay cables has become a concern in bridge engineering over the past decades. The excitation mechanism of RWIV remains unclear. Many researchers believe that the upper rivulet is crucial to RWIV. However, experimental study on rivulet is challenging and limited. The current study designs and tests a cable model of 160mm in diameter in an open jet wind tunnel. The upper rivulet movement and cable vibration are simultaneously measured. The importance of the upper rivulet in RWIV is directly demonstrated by alternately controlling the upper and lower rivulets. The characteristics of the upper rivulet movement and the effects of this movement on RWIV are investigated in detail. The experiment shows that the rivulet–cable system is coupled, which causes the cable and upper rivulet to vibrate at different amplitudes under the same wind speed. The upper rivulet harmonic movement changes the wind loading on the cable, causing the harmonic vibration of the cable, which in turn exerts a harmonic inertia force on the rivulet. A large vibration of the coupled system then develops.

Classification of the tripped cylinder wake and bi-stable phenomenon

Experimental investigation is conducted in the wake of a circular cylinder with two tripwires attached at azimuthal angle α = ±10° to 70° measured from the forward stagnation point at Reynolds numbers ( Re) = 2.5 × 10 3–6 × 10 4. The tripwire diameter was 0.045 d, where d is the cylinder diameter. Time-averaged drag ( C D ), fluctuating drag ( C D,rms ) and lift ( C L,rms ) were measured, along with Strouhal number ( St) and the flow structure in the wake. The flow is classified as five regimes based on present measurements and also those in literature. In Regime A, α < 20°, the forces, St and St–Re relationship are all similar to their counterparts in a plain cylinder wake. In Regime B, 20° ⩽ α ⩽ 35°, C D , C D,rms and C L,rms all decline considerably and St escalates with increasing α. In Regime C, 35° < α ⩽ 40°, C D , C D,rms and C L,rms plummet rapidly. In Regime D, 40° < α < 45°, the flow may occur in two distinct stable modes, which switches randomly from one to another; accordingly, the instantaneous drag and St display drastic up-and-down jumps. Regime E occurs at α = 45–70°, where C D , C D,rms and C L,rms are large and St is small. This regime may be further divided into two, viz. E 1 (45° ⩽ α < 60°), where C D , C D,rms and C L,rms grow and St decreases with increasing α, and E 2 (60° ⩽ α < 70°), where the dependence of the parameters on α is less pronounced. The bi-stable phenomenon (Regime D) is given special attention and its possible connection to the mechanism of well reported rain–wind-induced cable vibration is proposed.

Rain–wind-induced cable vibrations in the Alamillo cable-stayed bridge (Sevilla, Spain). Assessment and remedial action

Rain combined with wind action provoking vibration has been observed in the longest stays of the Alamillo cable-stayed bridge in Sevilla (Spain). The maximum displacements observed are in the order of magnitude of 0.5 m and have caused discomfort problems to the pedestrian circulation across the bridge. The paper shows the analytical and experimental studies carried out to analyse the possible solutions and also the steps developed to stop the vibration phenomenon. In 2004, a dynamic test in the cables was envisaged to measure the actual damping in the cables. It became clear that damping in the cables was very low and the solution required the installation of dampers. The damping devices had to be in accordance with the relevant aesthetic constraints of the structure. The installation of the damping devices took place during 2007. After the installation of the damping devices, a new dynamic test was carried out in February of 2008 to check if the level of damping introduced by the dampers was appropriate. During the tests performed in 2004, the natural frequencies of vibration were also obtained at the same time than damping. The comparison between the two sets of natural frequencies (1992 and 2004) allow to extract important conclusions about the correct performance and condition state of the bridge as well as the evolution of forces in the cables after 12 years of construction due to creep in the tower.

Mechanics in naturally compliant structures

In this study the mechanics of compliant structures (very light weight structures which do not have bending capability but have axial stiffness (tension)) in particular to spider web has been studied. The orb-web spider has evolved over the last 180 million years [Lin, L.H., Edmonds, D.T., Vollrath, F., 1995. Structural engineering of an orb-spider’s web. Nature 373, 146–148]. This long period of evolution has produced the present spider web, an elegant, natural, lightweight structure to efficiently resist different loads such as wind, insect impact, etc. It can function as a net for catching prey even if any element is broken. Nature has accomplished these tasks by optimizing its form of construction, and by making spider silk a biopolymer with superior elasticity and tensile strength. It is believed that spider webs are the most efficient structures engineered by nature. In this study it is tried to find why spider webs are so efficient. A FE model of an ideal spider web has been created using the FEMAP pre- and post-processing software, and analyzed using the ABAQUS non-linear FE code. Both the static and dynamic problems have been considered, and also the numerical and experimental techniques have been used. It has been tried to look at how stress is redistributed in the face of damage and how the loss of elements affects the dynamic response of the web and how the vibration due to insect impact is damp out. Finally the numerical simulations have been compared to physical experiments. In lieu of actual spider webs, artificial nets have been examined and its 1st natural frequencies for different cases have been measured by laser vibrometer. A FE model of the net has also been created in FEMAP and analyzed by ABAQUS. In both analyses, the same elements have been removed systematically from the center and the 1st natural frequencies have been determined. Prediction matches well with experiment. The results of this study may be used in light structures like cable-stayed bridges [Masura, M., Yokoyama, K., Toshio, M., 1989. Wind-induced cable vibration of cable-stayed bridges in Japan. In: Proceedings of Canada–Japan Workshop on Bridge Aerodynamics, Ottawa, pp. 101–110; Yoshimura, T., Inoue, A., Kaji, K.K., Savage, M.S., 1989. A study on the aerodynamic stability of the Aratsu Bridge. In: Proceedings of Canada–Japan Workshop on Bridge Aerodynamics, Ottawa, pp. 41–50] and space structures.

Cable Vibration Control using Magnetorheological Dampers

As the world's first implementation of magnetorheological (MR) smart damping technique in bridge structures, a total of 312 semi-active MR dampers (RD-1005, Lord Corporation) have recently been installed for rain–wind-induced cable vibration control on the cable-stayed Dongting Lake Bridge, China. This project has undergone several stages of in situ experiments and tests: (i) modal tests of undamped cables, (ii) forced vibration tests of MR-damped trial cables, (iii) monitoring of MR-damped and undamped cable responses under rain–wind excitations, (iv) comparative tests using different damper setups, (v) full installation, and (vi) field measurements and real-time control tests after the installation. After outlining the above six stages of the whole project and addressing the experience and lessons learned from both open-loop control and closed-loop control practices, this study focuses on the design considerations of implementing MR dampers for cable vibration control, taking into account the effects of the damper stiffness, damper mass, stiffness of damper support, nonlinearity of the damper, and sag and inclination of the cable. The research efforts make it possible to develop elaborate MR dampers specific for application to bridge stay cables.

Fluid dynamics around an inclined cylinder with running water rivulets

The formation of water rivulets running along an inclined circular cylinder and its effects on the near-wake were experimentally investigated. Water was released from the upper end of the cylinder at a volume flow rate Q. At an incoming wind speed U ∞ = 8 – 15 m / s , two water rivulets were observed near the flow separation points, running along the cylinder inclined at α = 45 ° for 0 ° ⩽ β ⩽ 90 ° , where β is the cylinder yaw angle, and both oscillating circumferentially. The dependence of the rivulet formation on U ∞ , Q and β is examined in detail. The quasi-periodic vortex street is observed intermittently with and without the presence of the rivulets. The rivulets cause an increase in the normalized dominant frequencies in the near wake and further lead to a significant increase in the drag coefficient, which is consistent with the violent vibration associated with the rain–wind-structure interactions. The effect of the rivulets on the near-wake vortices is investigated. It is found that the vortex strength grows by up to 60% as β increases from 0° to 30°. A mechanism for the rain–wind-induced cable vibration is proposed.

Experimental investigation of rain–wind-induced vibration of cables in cable-stayed bridges and its mitigation

Rain–wind-induced vibration of cables in cable-stayed bridges is presently a worldwide problem of great concern. Because it is sensitively influenced by many parameters, this peculiar phenomenon is difficult to be replicated in laboratory conditions; its mechanism has not been well explained yet. In this paper, the phenomenon of rain–wind-induced vibration of a cable model is successfully reproduced under actual rain conditions in a wind tunnel. The effects of several main factors, including the inclination angle, frequency and damping of the cable as well as the wind yaw angle, etc. on the characteristics of rain–wind-induced vibration are investigated in detail in the test. The countermeasures of double-spiral wires and dampers for the mitigation of the vibration are also experimentally studied. The results show that the size and twine direction and the pitch of the spiral wires twined on the surface of cables have great effects on the mitigation efficiency of rain–wind-induced vibration of cables.

Field observation of the full-scale wind-induced cable vibration

Wind-induced vibration of inclined cables of cable-stayed bridges is one of the most serious problems in bridge aerodynamics. Especially, the rain–wind induced vibration that can be explained as vortex-induced vibration at high reduced wind velocity has been reported at many cable-stayed bridges in the world. In order to clarify the characteristics and the mechanisms of the rain–wind induced vibration, experimental setup using full-scale cable model was constructed in the field, and aerodynamic behavior of this cable model was observed under various weather conditions. Then the vibration, which might be considered as the rain–wind-induced vibration, was observed.

Rain–wind-induced vibration of inclined cables at limited high reduced wind velocity region

Aerodynamic vibration of stayed cables, especially rain–wind-induced cable vibration, has been a rather serious problem on the design of cable-stayed bridges. This well-known phenomenon occurs at particular high reduced wind velocity regions and under raining condition. From results of wind tunnel tests, it might be explained as a vortex-induced vibration, which occurs at limited high reduced wind velocity region. Then, in this study, the effects of water rivulet and the wind turbulence on the vortex-induced vibration at high reduced wind velocity are investigated by wind tunnel tests, and the mechanism of the rain–wind-induced cable vibration is tried to be understood comprehensively. Furthermore, the role of Karman vortex in this vibration is discussed.

Response characteristics of wind excited cables with artificial rivulet

A wind tunnel investigation of response characteristics of cables with artificial rivulet is presented. A series of cable section models of different mass and stiffness and damping ratio were designed with artificial rivulet. They were tested in smooth flow under different wind speed and yaw angle and for different position of artificial rivulet. The measured response of cable models was then analyzed and compared with the experimental results obtained by other researchers and the existing theories for wind-induced cable vibration. The results show that the measured response of horizontal cable models with artificial rivulet could be well predicted by Den Hartog's galloping theory when wind is normal to the cable axis. For the wind with certain yaw angles, the cable models with artificial rivulet exhibit velocity-restricted response characteristics.

A Study on Countermeasures against Wind-Induced Cable Vibrations in Cable-Stayed Bridge by Changing Vibration Modes. 3rd Report. Design Method of a Control Device.

In order to suppress vibrations of stay cables in cable-stayed bridges, the authors developed a new vibration reduction called Changing vibration modes method using a permanent magnet. The authors have confirmed its effectiveness in former reports by both theoretical analyses and wind tunnel tests. In second report, the authors analyzed cable vibrations by taking account of only an unstable mode and clarified how the design parameters such as a gap and magnetic force affect the control efficiency. In this report, accuracy of the analysis is further improved by introducing the higher modes effects as an equivalent aerodynamic damping. Then, a design procedure of the parameters is proposed on the basis of the improved analysis, and its validity is shown by wind tunnel test results.

A Study on Countermeasures against Wind-Induced Cable Vibrations in Cable-Stayed Bridge by Changing Vibration Modes. 4th Report. Experimental Application to an Actual Cable.

In order to suppress vibrations of stay cables in cable-stayed bridges, the authors developed a new vibration reduction called Changing vibration modes method using a permanent magnet. With this method, growth of the unstable fundamental vibration mode is prevented by dissipating energy of higher stable modes. The authors have confirmed in former reports that the proposed effectively reduces the self-induced cable vibrations by both theoretical analyses and wind tunnel tests and design of the device was proposed. In this report, first, the design process of a prototype of a control device is described. Second, higher mode vibrations generated by the action of the device were confirmed from the results of free vibration tests. Finally, efficiency of the proposed countermeasure against rain-wind-induced vibrations of an actual cable is clarified.

A Study on Countermeasures against Wind-Induced Cable Vibrations in Cable-Stayed Bridge by Changing Vibration Modes. 2nd Report. Cable Vibration Analyses Taking Account of Gap Effect.

Vibrations of stay cables are often induced by wind because of their aerodynamic instability. They must be suppressed to prevent cable fatigue and to allay passenger fear. Although various countermeasures have been developed, totally effective one has not yet been established. The authors have proposed a new vibration reduction called Vibration modes changing method using a permanent magnet. A magnet installed near the end of the cable changes the vibration modes passively by repeating motions of constraining and releasing cables. With this method, growth of the unstable fundamental vibration mode is prevented by dissipating energy of higher stable modes. Comparing with other methods, it is expected to improve low temperature characteristics, maintenance and manufacturing cost. Considering only unstable fundamental vibration modes, the vibration analyses were carried out taking account of gap effects. The results agree well with wind tunnel tests and the design conditions were obtained.

Recent topics on bridge aerodynamics

This paper aims to describe the aerodynamic vibrations of various structural elements of bridges, which are particular issues at present. The aerodynamic countermeasures for those vibrations are also discussed considering the generation mechanisms of the aerodynamic instabilities. In this paper, an example of vortex-induced oscillation of bridge deck and its lesson are discussed. Next, the wind-induced cable vibration and its aerodynamic countermeasures are reviewed. Then, the aerodynamic characteristics on two edge girders and their feasibility for application to long span cable-stayed bridges are considered. Furthermore, the bridge decks for future long span bridges are proposed and their aerodynamic characteristics are also discussed.

A Study on Countermeasures against Wind-Induced Cable Vibrations in Cable-Stayed Bridge by Changing Vibration Modes.

Vibrations of stay cables are often induced by wind because of their aerodynamic instability. They must be suppressed to prevent cable fatigue and to allay passenger fear. Although various countermeasures have been developed, totally effective one has not yet been established. In this paper, the authors propose a new method using a permanent magnet. A magnet installed near the end of the cable changes the vibration modes passively by repeating motions of constraining and releasing cables. With this method, growth of the unstable fundamental vibration mode is prevented by dissipating energy of higher stable modes. Comparing with other methods, it is expected to improve low temperature characteristics, maintenance and manufacturing cost. After decribing the principle, fundamental studies on energy transferring mechanism were carried out and it was verified that the lower modes energy is distributed to the higher modes when the cable is released from the magnet. The effectiveness of this method was confirmed by wind tunnel tests and numerical simulations.

永久磁石を使った斜張橋ケーブルの制振技術

永久磁石を使った斜張橋ケーブルの制振技術