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

Significance Statement

A great concern in the engineering community is the vulnerability of inclined bridge stay cable when subjected to excitation by natural wind. This study is proposed to examine the susceptibility of stay cables on cable-stayed bridges to practical wind conditions. It employs a three-dimensional aeroelastic model and numerical solution technique to explore the excitation mechanisms of and contributing factors to inclined cable galloping. The violent cable motion under various unsteady mean wind conditions are investigated, which is found to be triggered by an opposite-phase relation between the aerodynamic force along the direction of cable motion and the relative wind speed in the critical flow regime.

The vulnerability of stay cables on cable-stayed bridges to environmental excitations, such as natural wind, wind combined with rain, is mainly due to their low inherent damping and high lateral flexibility. The assessment of pre-existing motion of stay cables and exposure to atmospheric boundary layer type wind speed profile is essential to find their respective impact on the growth of galloping response. The various types of unsteady winds such as speed of winds increasing from sub-critical to critical range, decrease in speed from critical to sub-critical range and ideal representation of wind gusts presence are considered in the assessment process.

The observation by the authors, Dr. Arash Raeesi, Professor Shaohong Cheng and Professor David Ting from the University of Windsor in Canada, showed that the cables were susceptible to wind excitations in the absence of rain when wind speed reaches the critical Reynolds number regime. This type of large amplitude wind-induced cable vibration is termed as dry inclined cable galloping. The most favorable conditions for galloping development are found to be when a cable is subjected to uniformly distributed steady wind in the critical Reynolds number range sustained over a sufficient period of time. The research work is now published in Journal of Sound and Vibration.

 The mechanism of cable galloping contains three key elements namely emergence of critical Reynolds number regime, span-wise correlation of aerodynamic forces on the cable and the sustained duration of critical flow condition. Aerodynamic forces acting on the cable highly depends on the Reynolds number. In the critical Reynolds number regime, the emergence of drag crisis and the steady non-zero lift force within a narrow range leads to negative aerodynamic damping.

 In other words, the aerodynamic forces become very sensitive to Reynolds number variation within the critical regime. It decreases with increase of Reynolds number and vice versa. Net increase of the peak amplitude in each cable vibration cycle is observed when there is a 180 degree out-of-phase relation between the wind velocity and the aerodynamic force in the critical Reynolds number range. It would cause a gradual build-up of cable response and eventually lead to galloping. This is believed to be the actual triggering mechanism of dry inclined cable galloping.

 The authors validated the proposed three-dimensional aeroelastic model and the finite difference solution scheme by comparing the cable free vibration response with those in the literature. The aerodynamic response of a sample cable with moderate sag and relatively low bending stiffness is analysed by applying different initial conditions and various types of unsteady wind conditions.

 The effect of flow unsteadiness is found to have a dual effect on the wind-induced response of a dry inclined cable depending on its fluctuation frequency. While the high frequency turbulence components in the flow would advance the critical Reynolds number range and thus increase the possibility of galloping occurrence at lower wind speed, the relatively lower frequency fluctuation components would have a stabilizing effect on the cable response.

The analytical model proposed by the authors in this study will improve our understanding on the excitation mechanisms and contribution factors associated with dry inclined cable galloping and clarify the onset conditions of this type of cable aerodynamic instability phenomenon on site.  

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

About the author

Dr. Arash Raeesi is a research council officer at aerospace portfolio of National Research Council, Canada since 2016. Within the past 8 years, Arash has been involved in multiple bluff body aerodynamics and wind engineering research projects such as study of aeroelastic instabilities of stay cables on cable-stayed bridges. Arash was born in Tehran, Iran in 1983. In 2001, he was enrolled in the University of Tehran where he obtained the Bachelor of Science in Mechanical Engineering in 2006. In winter of 2009, Arash graduated from the University of Windsor with a Master of Science degree in Mechanical Engineering.

He received his doctoral degree in Civil Engineering from University of Windsor in 2015, researching on wind-induced galloping of stay cables under unsteady wind conditions.  

About the author

Shaohong Cheng is an Associate Professor in the Department of Civil and Environmental Engineering at the University of Windsor. She is a Professional Engineer of Ontario and member of American Society of Civil Engineers and International Association for Bridge and Structural Engineering. Dr. Cheng worked on flutter of long-span bridges during her graduate studies. Before joining the University of Windsor, she was in charge of a wind tunnel study on wind-induced cable vibrations in collaboration with the Federal Highway Administration of US and the National Research Council Canada, and also worked as a senior consulting engineer in Gradient Wind Engineering Inc..

Dr. Cheng is the founder of the Boundary Layer Wind Tunnel Laboratory at the University of Windsor. She conducts research and supervises students in a broad range of projects, mainly in the areas of bluff body aerodynamics, fluid-structure interaction, vibration control and concrete technology.

In recent years, her research is focused on Wind-induced response of structures, in particular, the bridge stay cables; Mitigating excessive stay cable vibrations using external dampers, cross-ties and hybrid systems; Mechanisms associated with dry inclined cable galloping and high-speed vortex excitation; Enhancing the aerodynamic stability of a new small ducted-fan type VTOL UAV model for precision agriculture; Simulating atmospheric boundary layer effect in the wind tunnel; Shear strengthening of prestressed precast concrete hollow core slabs using carbon fibre reinforced polymer.  

About the author

David S-K Ting worked on Combustion and Turbulence (Premixed Turbulent Flame Propagation) during his graduate years. He then ventured into Convection Heat Transfer and Flow-Structure Interactions, prior to joining University of Windsor. Professor Ting is the founder of the Turbulence & Energy Laboratory. Dr. Ting supervises students on a wide range of research projects primarily in the Energy Conservation and Renewable Energy areas.

Specifically, his recent research includes Convective Cooling of Solar PV Panels, Enhancing the Performance of Geothermal Heat Exchanger, Wind Farm Analytics, Monitoring, and Performance Prediction, Smart Water, Mitigation of Flow-Induced Vibrations, Aerodynamics, Energy Systems, Heat Transfer, and Wave Energy. Fundamentally, his love is still faithfully on Flow Turbulence.  

Journal Reference

Arash Raeesi1, Shaohong Cheng1 , David S.-K. Ting2, Application of a three-dimensional aeroelastic model to study the wind-induced response of bridge stay cables in unsteady wind conditions, Journal of Sound and Vibration, Volume 375, 2016, Pages 217–236.

Show Affiliations
  1. Department of Civil and Environmental Engineering, University of Windsor, 401 Sunset Avenue, Windsor, Ontario, Canada N9B 3P4.
  2. Department of Mechanical, Automotive and Materials Engineering, University of Windsor, 401 Sunset Avenue, Windsor, Ontario, Canada N9B 3P4.



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