Rain Wind-induced Vibration Research Articles

An investigation of rain-wind induced vibrations on stay cables in a novel range of operating conditions

The large-scale rain-wind induced vibration (RWIV) dynamic test rig at the National Research Council Canada (NRC) was used in the current work to evaluate the vibration characteristics of a 0.218 m diameter smooth stay cable, for two cable inclinations and a wide range of yaw-angle conditions. The structural damping ratio was in the range of 0.05% to 0.11% and the heave frequency was approximately 1.23 Hz for a cable with a moving mass of 217 kg. The presence of RWIV was investigated at an inclination angle of 30° from the horizontal over a yaw-angle range of 25° to 45°and for an inclination angle of 55° over a yaw-angle range of −40° to ＋45°. An upper rivulet was present when vibrations were observed. For positive yaw angles, the upper rivulet was characterized by a thin line of water, approximately 5 to 10 mm wide, running along the entire length of the inclined cable on the windward side and moving along the cable span with a serpentine motion. For negative yaw angles, the upper rivulet was located near top of the cable or on the leeward sector of the cable, was wider than the rivulets observed for positive yaw angles, and was not observed to move in a serpentine motion. RWIVs were observed for each yaw angle that was investigated, including at negative yaw angles, with a maximum amplitude of motion of ±150 mm (∼0.7D). The direction of the rain impingement was an important factor affecting the formation and characteristics of the upper rivulet at the surface of the cable and, for the onset for vibrations. RWIVs were observed for wind speeds between 5 and 12 m/s. The Reynolds number corresponding to the onset of RWIV tended to increase with larger yaw angles in the positive yaw-angle range. At an inclination angle of 30°, the onset of RWIV ranged from 1.2×105 at a yaw of 25° to 1.4×105 at a yaw of 45° while at a cable inclination angle of 55°, the onset of RWIV ranged from 1.08×105 at a yaw of 25° to 1.25×105 at a yaw of 40°. The onset of vibrations for a yaw angle of 0° was at 0.77×105 for a cable inclination of 55°. RWIV was initiated at lower Reynolds numbers at an inclination angle of 55° for negative yaw angles, with vibrations observed at wind speeds as low as 5 m/s (Reynolds number of 0.7×105). The results confirmed the presence of RWIV in well-understood conditions and have effectively expanded the range of conditions over which RWIV has been observed in a wind tunnel. The expanded range over which RWIV was observed includes vibrations at an inclination angle of 55°, vibrations at a yaw angle of 0°, and vibrations at negative yaw angles from −10° to −40°.

Influence of reduced drag load on stay cables on the construction cost of cable-stayed bridges: Two study cases

Rain–wind–induced vibrations (RWIVs) can cause the large-amplitude vibration of flexible cables in cable-stayed bridges; such vibration is one of the engineering safety problems that must be resolved. Currently, aerodynamic measures, such as dimples and spirals, are typically used as measures for suppressing vibration in stay cables. By calculating and comparing the equivalent static wind loads (ESWLs) of six typical cable-stayed bridges, the proportion of ESWL acting on the cable to that acting on the entire bridge increases approximately linearly with the bridge span. Hydrophobic coating can effectively suppress RWIVs and evidently relieve the ESWL. Hence, compared with the commonly used aerodynamic measures with surface roughness, this coating has a considerable potential as an alternative for suppressing vibration. Based on the foregoing, the wind resistance design optimization of two actual cable-stayed bridges with main spans of 420 and 1160 m is implemented to investigate the construction costs of cable wind load reduction. After optimization, the structural responses of the main towers are reduced by 4%–12%, and the optimized tower and foundation sizes are reduced by 5%–8%. The optimization for the two bridges exceed 5% and 7%, respectively. The construction investment savings are approximately 2.3 million and 7.2 million USD, respectively. These values further improve with increasing bridge span and design wind speed.

Effect of the upper rivulet on the aerodynamic forces and vibration of stay cables in the critical Reynolds number range

During the rain-wind-induced vibration (RWIV) process, a water rivulet forms on the surface of stay cables, and the upper rivulet is considered to be an important factor in RWIV formation. The cables also exhibit galloping in the absence of rain. To reveal the effect of a rivulet on galloping and help explain the mechanism of RWIV, from the viewpoint of the Reynolds number effect, a cylinder with an artificial rivulet at multiple angles was tested in wind tunnel experiments. The results show that the rivulet has a significant effect on the aerodynamic force coefficients, and the increase in the rivulet position decreases the onset Reynolds number of TrBL0-1 transition. A large-angle rivulet limits reattachment on the upper surface of the model, and the vortex appears in TrBL1. Due to reattachment, bistability can be observed in the TrBL0-1 and TrBL1-2 transitions, and the wake vortex is suppressed. During the formation of a separation bubble, the aerodynamic forces change dramatically, which affects the aerodynamic damping of the cables and induces galloping instability in most cases. The condition of reattachment on the upper surface of cables may be an important reason for RWIV occurrences.

A New Method to Reduce Rain–Wind-Induced Vibration in Cable Sleeve of Cable-Stayed Bridges and Modeling in a Wind Tunnel

A New Method to Reduce Rain–Wind-Induced Vibration in Cable Sleeve of Cable-Stayed Bridges and Modeling in a Wind Tunnel

Theory of rain–wind induced vibration of stay cables: Toward unsteady and fully coupled modeling

Large-amplitude rain–wind induced vibration (RWIV) is a complex fluid–structure interaction process that may develop if light rainfall and moderate wind act concurrently on long stay cables of a cable-stayed bridge. However, its dynamic characteristics and excitation mechanism are remained an open question. Recently, a theoretical framework for the analysis of RWIV was proposed, based on a quasi-steady-state approximation of the movement of upper rivulet, to reveal the main features of the dynamic process of RWIV. In the present study, we further consider the unsteady and dynamic behaviors of the moving upper rivulet and its coupling effects with the cable movement. The periodic mass, circumferential movement of the upper rivulet was modeled based on experimental observations. The theoretical results are then validated by comparison with experimental results. In addition, some parameters that influence RWIV are investigated in detail. The augmented theory in the present study gives a more accurate model and promotes more reliable evaluations of the dynamic behaviors of RWIV of stay cables.

A revised Scruton number on rain-wind-induced vibration of stay cables

Rain-wind-induced vibration (RWIV) is a typical large-amplitude vibration for stay cables. Due to the complex influencing factors and unclear mechanism, a Scruton number criterion Sc is usually adopted for RWIV-resistant design. However, this criterion has proved to be too conservative. The original Sc number characterized independently by mass and damping can not accurately reflect RWIVs' characteristics, and it is still difficult to compare test results with field measurement using the traditional Sc number. In this work, cable vibrations were studied through wind tunnel experiments and field measurements, and it is concluded that aerodynamic damping varies with mass also influences cables’ responses. The variation law of aerodynamic damping is analyzed by wind tunnel experiments, while the total damping of an actual cable of the Jintang Bridge has been identified by an empirical mode decomposition (EMD) method and the random decrement technique (RDT). A revised Sc* number with clear physical meaning considering aerodynamic damping is proposed. The aerodynamic damping for lighter models can be up 10 times that of prototypes, which makes the Sc* numbers the same order of magnitude. The results of different wind tunnel experiments and field measurements show that most large-amplitude vibrations occur at Sc* = 1–2.5. And, it is necessary to consider aerodynamic damping for more comparable work and more accurate prediction.

Optimization of Multiple Helical Fillets Surface to Suppress Rain-wind Vibration of Stay Cables: A Wind Tunnel Investigation

Aims: To develop a new cable surface for control rain wind induced cable vibration of stay cable. Background: Stay cables are light and vulnerable structures. Therefore, it can be easily excited by wind or rain wind interaction. Stay cables wrapped with a single helical fillet have been proposed so far. However, these countermeasures could prevent cable vibration well, especially in dry conditions. Objective: Therefore, the objective of this research is to develop a new cable surface to control not only RWIV but also dry galloping of stay cable. Methods: A wind tunnel test will be used to investigate the RWIV characteristics and its new countermeasure. Results: First, a rain wind-induced vibration of circular stay cable was reproduced in a wind tunnel environment. The effect of upper and lower water rivulets was examined to understand their role on RWIV better. A rainfall simulator was employed to generate artificial rainfall for two different wind tunnel experiments. Finally, to control the RWIV of stay cables, novel multiple helical surface fillets were used. The upper and lower rain rivulets can play a significant role in energizing the RWIV. It was also found that the multiple helical surface fillets can suppress the cable vibration well both in wet and dry conditions. Conclusion: Multiple helical fillets cable surface could successfully prevent both the RWIV and dry galloping. To fabricate helical fillet cable to control cable vibration, 04 to 12 fillets with sizes ranging from 3mmx7.5mm to 5mmx7.5mm and a pitch of 2.95D-4.78D (D: cable diameter) are the most influential parameters and suggested herewith for practical application.

Theory of rain-wind-induced vibration of stay cables: A quasi-steady-state approximation

Rain-wind-induced vibration (RWIV) of stay cables in cable-stayed bridges is jointly induced by rainfall and incoming wind. It is a major concern to the bridge engineering community due to its very large vibration amplitude. Yet the characteristics and mechanism of RWIV have not been understood completely. In particular, a theoretical model that can well describe the RWIV is urgently needed for amplitude prediction in engineering applications. Following a recent experimental work, we propose a theoretical framework for the analytical analysis of RWIV in the present study. The moving upper rivulet, which plays a crucial role in the excitation of RWIV, is modeled with a quasi-steady-state approximation. The analytical and numerical results are first compared with the experimental data to validate the theory. Then, the effects of some key parameters, including cable mass, frequency, damping ratio, and dynamic upper rivulet, on RWIV are investigated in detail with the theoretical framework. The model in the present study provides quick and reliable evaluations of the vibration amplitude and influencing parameters of RWIV, without performing time-consuming experiments in wind tunnel or computational fluid dynamics simulations.

Monitoring-based analysis of wind-induced vibrations of ultra-long stay cables during an exceptional wind event

Ultra-long stay cables characterized as high flexibility are prone to large-amplitude vibrations. Much attention has been paid to the vibrations of stay cables under normal wind conditions in the past decades, while the dynamic response under extreme winds is reported rarely. This study investigates the exceptional wind-induced vibration of the stay cables of a kilometer-level cable-stayed bridge based on the monitoring data. The mean wind velocity and extreme wind duration are firstly obtained using the wind records of the structural health monitoring system (SHMS). The effects of the turbulence intensity and mean wind velocity on the cable vibrations are then analyzed. To explore the motion trajectory features, the in-plane and out-of-plane dynamic displacements are estimated by an acceleration-based approach. Besides, the modal properties, including the frequencies and damping ratios, are identified. The result shows that the stay cables present multi-modal vibrations with frequencies higher than 3 Hz, which is different from rain-wind-induced vibration (RWIV). The out-of-plane vibration amplitude under the extreme wind is much larger than that of the in-plane due to the absence of dampers. Furthermore, the out-of-plane damper is suggested to mitigate the large-amplitude vibration of ultra-long stay cables under exceptional winds.

On the coupling mechanism of rain–wind two-phase flow induced cable vibration: A wake-dynamics perspective

Large amplitude rain–wind induced vibration (RWIV) of stay cables of long-span cable-stayed bridges has been a major concern in the past three decades, yet its excitation mechanism has not been clarified thoroughly. Recent numerical simulations and experimental work showed that when the RWIV of a cable is developing, the dominant frequency of its unsteady lift forces is notably decreased, i.e., the conventional Strouhal law of cylinder flow is obeyed. In some experimental studies, however, the small-scale vortical structures, which are believed to be closely associated with the low-frequency fluctuating components, are visualized qualitatively in the cable wake during the RWIV. In the present work, the first experimental observation of the dynamic wake behind a cable during the RWIV is presented. The RWIV is reappeared based on a stay cable model supported by springs in wind tunnel tests. The dynamic characteristics of the water rivulet on the upper surface of the cable are recorded by a high-speed camera, and the detailed wake flow of the cable is captured by employing the high-speed particle image velocimetry technique. We focus on the low-frequency synchronization between the cable vibration, upper-rivulet movement, and the wake dynamics to investigate the excitation mechanism of the RWIV. A three-phase (gas–liquid–solid) coupling scenario is finally proposed to explain this interesting phenomenon as low-frequency resonance between fluids and the cable structure.

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 Phenomena in Long-Span Cable-Supported Bridges: A Comparative Review of Wind Tunnel Tests and Computational Fluid Dynamics Modelling

Engineers, architects, planners and designers must carefully consider the effects of wind in their work. Due to their slender and flexible nature, long-span bridges can often experience vibrations due to the wind, and so the careful analysis of wind effects is paramount. Traditionally, wind tunnel tests have been the preferred method of conducting bridge wind analysis. In recent times, owing to improved computational power, computational fluid dynamics simulations are coming to the fore as viable means of analysing wind effects on bridges. The focus of this paper is on long-span cable-supported bridges. Wind issues in long-span cable-supported bridges can include flutter, vortex-induced vibrations and rain–wind-induced vibrations. This paper presents a state-of-the-art review of research on the use of wind tunnel tests and computational fluid dynamics modelling of these wind issues on long-span bridges.

A new large-scale dynamic rig to evaluate rain-wind induced vibrations on stay cables: Design and commissioning

Cable-stayed bridges are exposed to different weather conditions including wind and rain. The wind can excite the cables causing them to vibrate and this effect can be amplified in the presence of rain. There are a limited number of facilities worldwide capable of testing rain-wind induced vibration (RWIV) on large stay cable models. A new RWIV test rig has been developed for use in the National Research Council 9 ​m Wind Tunnel. The RWIV test rig and rain system were commissioned in July–August 2019. The commissioning study demonstrated the ability of the rig to generate large-amplitude wind-induced vibrations on a cable with a length of 5 ​m and a length-to-diameter ratio of 23.

Effects of bending stiffness and support excitation of the cable on cable rain-wind induced inclined vibration

The main objective of this paper is to investigate the responses of the inclined cable due to rain-wind induced vibration (RWIV) considering the bending stiffness and support excitation of the cable. The single-degree-of-freedom (SDOF) model is employed to determine the aerodynamic forces. The 3D model of a cable subjected to RWIV is developed using the linear theory of the cable oscillation and the central difference algorithm in which the influences of wind speed change according to the height above the ground, bending stiffness, and support excitation of the cable are considered. The numerical results showed that the cable displacement calculated by considering cable bending stiffness in RWIV is slightly smaller than in the case of neglecting it. And, the cable diameter had a nonlinear relationship with cable displacement, where when both diameter and mass per unit length of cable increase cable displacement will decrease. In addition, the periodic oscillation of cable supports extremely increases the amplitude of RWIV if its frequency is nearby that of the cable.
 Keywords:
 3D model; inclined cable; rain-wind induced vibration; rivulet; analytical model; vibration.

Effects of Time-Varying Mass on Stability of High-Voltage Conductor in Rain–Wind Condition

Abstract Although unanticipated low-frequency vibrations frequently happen on high-voltage conductors under the simultaneous occurrence of wind and rain, the source of these vibrations is not well known. Many studies focus on the impact of rain loads on the high-voltage conductor but very few examine the effects of time-varying mass. Raindrops hitting high-voltage conductors may partially stay on their surface and form rivulets or ridges. As the adhered raindrops may be blown or shaken off, the mass of the rivulets will vary with time. In order to investigate how the time-varying mass of the rivulets affects conductor motion, an analytical model with time-varying mass is established, which leads to the statement of an instability criterion. The vibration characteristics and instability of a high-voltage conductor with fixed and movable rivulet are discussed. The results show that the time-varying mass ratio may affect the peak vibration amplitude, and the unstable zone of the conductor with moveable upper rivulet is much wider than that with fixed upper rivulet, and the rain–wind-induced vibration occurs more easily than Den Hartog galloping. Such comparative studies may prove valuable as they enhance the understanding of the mechanism of the rain–wind induced instability of the high-voltage conductors.

Six‐degree‐of‐freedom generalized displacements measurement based on binocular vision

Due to their large flexibility and small damping ratios, harmful vibrations could happen on cables under some external excitations, as for instance the rain–wind-induced vibration, which comes with a translational and rotational coupling. An experimental study of the phenomenon would be quite important in view of an appropriate design. However, the available rotational measurement approaches are not suitable for measuring the rotation of cable, because the installation of such devices alters the structural mechanical properties. Recently, low-cost vision-based structural displacement measurement methods have been widely used due to their flexible deployment and the noncontact measurement feature. But they cannot measure the rotational displacements directly. This paper proposes a rotational generalized displacement measurement method based on a binocular vision assisted by a coded cylinder. The three-dimensional coordinates of the coded points are acquired according to photogrammetry schemes. The cylinder centroid and its direction vector are obtained by a cylindrical fitting. Eventually, the translational and rotational generalized displacements are derived. In the cylinder fitting stage, one optimizes the cylinder model parameters via differential search. Experimental verifications are carried out to demonstrate that the proposed six-degree-of-freedom (6-DOF) generalized displacement measurement is feasible.

A three-dimensional model for rain-wind induced vibration of stay cables in cable-stayed bridges

In this paper, the effects of wind velocity according to height above the ground on the rain-wind induced vibration (RWIV) of stay cables are investigated. RWIV of the cable is modeled using the linear theory of cable vibration and the central difference algorithm. The wind speed profile according to height above the ground, which affects both aerodynamic forces acting on the cable and the oscillation of the rivulet on the cable surface, is taken into account in the theoretical formulation. The fourth-order method Runge-Kutta is used for solving the system of differential equation of the cable oscillation. The proposed 3D model of the stay cable is then used to assess the effects of wind velocity distribution on cable RWIV. The results obtained in this study showed that in most current cable-stayed bridges, in which the height of pylons is lower than 200 m, the change of wind velocity according to the height above the ground should be included in RWIV analyses.
 Keywords:
 stay cable; rain - wind induced vibration; rivulet; analytical model; vibration.

Vibration characteristics identification of ultra-long cables of a cable-stayed bridge in normal operation based on half-year monitoring data

The Sutong Bridge with a span of 1088 m is supported by 272 cables, whose lengths range from 152.85 m to 576.77 m (the longest in the world). The half-year vibration acceleration data of two cables from structural health monitoring system (SHMS) is analysed, in conjunction with the wind field data, weather data and vehicle data to explore and three types of cable vibrations. The large-scale cable vibration is mainly rain-wind-induced vibrations (RWIV) when the wind direction lies in an angular range of 40°–80° relative to the cable axis, and the bridge-deck wind velocity is 4–20 m/s. The ultra-long cable also experiences in-plane vibrations, which satisfy many characteristics of vortex-induced vibrations (VIVs). Cable VIV occurs only when the bridge-deck wind velocity 4–8 m/s, with the frequency ranging from 9.5 Hz to 10 Hz. The daily small-amplitude vibration of the cables and steel girder is mainly induced by the passage of heavy trucks. There exists a positive correlation between the number of heavy trucks and the vibration level. Based on the characteristics and occurrence probabilities of these three types of cable vibrations, corresponding measures are suggested for the maintenance of ultra-long cables.

Experimental investigation on mechanism and mitigation of rain–wind-induced vibration of stay cables

Rain–wind-induced vibration is one of the most severe vibrations for stay cables in long-span bridges. To clarify the mechanism of cable vibration and its aerodynamic countermeasures under two unfavorable refined rain–wind environments, wind tunnel tests were systematically conducted on cable sectional models with various surface processing schemes, including smooth surface, spiral protuberances, spiral dimples, straight dimples, and polyurea painting. Rivulet formation by cable vibrations under two unfavorable environments are discussed, and differences between mechanisms are preliminarily classified. The above schemes were investigated to determine their effectiveness in mitigating vibrations. Spiral protuberances had significant mitigating effects on cable vibration, and spiral protuberances of 0.011 height and 0.43 intervals nondimensionalized by the diameter of the cable were good enough to prevent rain–wind-induced vibrations. The effectiveness of dimples strongly depended on their arrangement on the cable surfaces. Polyurea painting reduced the possibility of large-amplitude vibration, but it also changed the unfavorable environmental conditions.

Parameter identification of wind-induced buffeting loads and onset criteria for dry-cable galloping of yawed/inclined cables

Cables of suspension, cable-stayed and tied-arch bridges, suspended roofs, and power transmission lines are prone to moderate to large-amplitude vibrations in wind because of their low inherent damping. Structural or fatigue failure of a cable, due to these vibrations, pose a significant threat to the safety and serviceability of these structures. Over the past few decades, many studies have investigated the mechanisms that cause different types of flow-induced vibrations in cables such as rain-wind induced vibration (RWIV), vortex-induced vibration (VIV), iced cable galloping, wake galloping, and dry-cable galloping that have resulted in an improved understanding of the cause of these vibrations. In this study, the parameters governing the turbulence-induced (buffeting) and motion-induced wind loads (self-excited) for inclined and yawed dry cables have been identified. These parameters facilitate the prediction of their response in turbulent wind and estimate the incipient condition for onset of dry-cable galloping. Wind tunnel experiments were performed to measure the parameters governing the aerodynamic and aeroelastic forces on a yawed dry cable. This study mainly focuses on the prediction of critical reduced velocity (RVcr) as a function of equivalent yaw angle (β*) and Scruton number (Sc) through measurement of aerodynamic-damping and stiffness. Wind tunnel tests using a section model of a smooth cable were performed under uniform and smooth/gusty flow conditions in the AABL Wind and Gust Tunnel located at Iowa State University. Static model tests for equivalent yaw angles of 0–45° indicate that the mean drag coefficient (CD) and Strouhal number (St) of a yawed cable decreases with the yaw angle, while the mean lift coefficient (CL) remains zero in the subcritical Reynolds number (Re) regime. Dynamic one degree-of-freedom model tests in across-wind and along-wind directions resulted in the identification of buffeting indicial derivative functions and flutter derivatives of a yawed cable for a range of equivalent yaw angles. Empirical equations for mean drag coefficient, Strouhal number, buffeting indicial derivative functions and critical reduced velocity for dry-cable galloping are proposed for yawed cables. The results indicate a critical equivalent yaw angle of 45° for dry-cable galloping. A simplified design procedure is introduced to estimate the minimum damping required to arrest dry-cable galloping from occurring below the design wind speed of the cable structure. Furthermore, the results from this study can be applied to predict the wind load and response of a dry cable at a specified wind speed for a given yaw angle.