A Combined Control Strategy for Vibration Mitigations of a Suspension Bridge Induced by Vehicle Braking Force


  • Meng-Gang Yang School of Civil Engineering, Central South University, No. 68 Shaoshan South Road, Changsha 410075, PR China
  • Chun-Sheng Cai Dept of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA
  • Biao Wei School of Civil Engineering, Central South University, No. 68 Shaoshan South Road, Changsha 410075, PR China




suspension bridge, vehicle braking force, viscous damper, friction pendulum bearing, combined control, vibration mitigation


In order to mitigate the excessive longitudinal displacement responses of suspension bridge girders induced by vehicle braking force, as one of the possible dynamic loadings, a combined control strategy consisting of viscous dampers and friction pendulum bearings is developed in this paper. Firstly, the vehicle composition and the braking force models of the Pingsheng Bridge are obtained by traffic survey and testing results, respectively. Then, the vibration response analysis for the bridge under the braking force is implemented using the MIDAS finite element model. Furthermore, viscous dampers and friction pendulum bearings are separately employed to reduce the vibration responses. The influence matrix method is first used to determine the optimal parameters of viscous dampers. Finally, the effect of the combined control strategy for the vibration control is investigated. The numerical analysis results indicate that utilizing the influence matrix method for the parameter optimization of viscous dampers is feasible and effective. It is also shown that the longitudinal displacement response of the Pingsheng Bridge subjected to the vehicle braking force can be effectively mitigated by viscous dampers, friction pendulum bearings or the combined control with the optimized parameters, and the combined control outperforms the viscous dampers or the friction pendulum bearings alone.


Apaydin, N. M. 2010. Earthquake Performance Assessment and Retrofit Investigations of Two Suspension Bridges in Istanbul, Soil Dynamics and Earthquake Engineering 30(8): 702–710. http://dx.doi.org/10.1016/j.soildyn.2010.02.011

Ates, S.; Bayraktar, A.; Dumanoglu, A. A. 2006. The Effect of Spatially Varying Earthquake Ground Motions on The Stochastic Response of Bridges Isolated with Friction Pendulum Systems, Soil Dynamics and Earthquake Engineering 26(1): 31–44. http://dx.doi.org/10.1016/j.soildyn.2005.08.002

Cantero, D.; Gonzalez, A.; OBrien, E. J. 2011. Comparison of Bridge Dynamic Amplifications due to Articulated 5-axle Trucks and Large Cranes, The Baltic Journal of Road and Bridge Engineering 6(1): 39–47. http://dx.doi.org/10.3846/bjrbe.2011.06

Cheng, S. H.; Darivandi, N.; Ghrib, F. 2010. The Design of An Optimal Viscous Damper for A Bridge Stay Cable Using Energybased Approach, Journal of Sound and Vibration 329(22): 4689–4704. http://dx.doi.org/10.1016/j.jsv.2010.05.027

Hart, G. C.; Jain, A.; Ekwueme, C. G. 2010. Smart Buildings: Viscous Dampers for A Tall Twisting Tower, Structural Design of Tall and Special Buildings 19(4): 373–396. http://dx.doi.org/10.1002/tal.608

Hoseini, S. M. S.; Fathi, M.; Vaziri, M. 2009. Controlling Longitudinal Safe Distance between Vehicles, Promet-Traffic & Transportation 21(5): 303–310. http://dx.doi.org/10.7307/ptt.v21i5.245

Hwang, J. S.; Wang, S. J.; Huang, Y. N.; Chen, J. F. 2007. A Seismic Retrofit Method by Connecting Viscous Dampers for Microelectronics Factories, Earthquake Engineering and Structural Dynamics 36(11): 1461–1480. http://dx.doi.org/10.1002/eqe.689

Hwang, J. S.; Tseng, Y. S. 2005. Design Formulations for Supplemental Viscous Dampers to Highway Bridges, Earthquake Engineering and Structural Dynamics 34(13): 1627–1642. http://dx.doi.org/10.1002/eqe.508

Jangid, R. S. 2008. Stochastic Response of Bridges Seismically Isolated by Friction Pendulum System, Journal of Bridge Engineering 13(4): 319–330. http://dx.doi.org/10.1061/(ASCE)1084-0702(2008)13:4(319)

Krishnamoorthy, A. 2011. Variable Curvature Pendulum Isolator and Viscous Fluid Damper for Seismic Isolation of Structures, Journal of Vibration and Control 17(12): 1779–1790. http://dx.doi.org/10.1177/1077546310384640

Liu, J.; Qu, W. L.; Pi, Y. L. 2010. Active/Robust Control of Longitudinal Vibration Response of Floating-Type Cable-Stayed Bridge Induced by Train Braking and Vertical Moving Loads, Journal of Vibration and Control 16(6): 801–825. http://dx.doi.org/10.1177/1077546309106527

Martinez-Rodrigo, M. D.; Lavado, J.; Museros, P. 2010. Dynamic Performance of Existing High-Speed Railway Bridges Under Resonant Conditions Retrofitted with Fluid Viscous Dampers, Engineering Structures 32(3): 808–828. http://dx.doi.org/10.1016/j.engstruct.2009.12.008

Panchal, V. R.; Jangid, R. S. 2009. Seismic Response of Structures with Variable Friction Pendulum System, Journal of Earthquake Engineering 13(2): 193–216. http://dx.doi.org/10.1080/13632460802597786

Peng, Y. H.; Wang, L. M. 2003. A Study on The Simulation of Vehicle’s Braking Process, Journal of Fuzhou University (Natural Science) 31(2): 182–185 (in Chinese).

Qu, W. L.; Qin, S. Q.; Tu, J. W.; Liu, J.; Zhou, Q.; Cheng H.; Pi, Y. L. 2009. Intelligent Control for Braking-induced Longitudinal Vibration Responses of Floating-Type Railway Bridges, Smart Materials and Structures 18(12): 125003. http://dx.doi.org/10.1088/0964-1726/18/12/125003

Wang, X. Y.; Ni, Y. Q.; Ko, J. M.; Chen, Z. Q. 2005. Optimal Design of Viscous Dampers for Multi-Mode Vibration Control of Bridge Cables, Engineering Structures 27(5): 792–800. http://dx.doi.org/10.1016/j.engstruct.2004.12.013

Yang, M. G.; Li, C. Y.; Chen, Z. Q. 2013. A New Simple Non-linear Hysteretic Model for MR Damper and Verification of Seismic Response Reduction Experiment, Engineering Structures 52: 434–445. http://dx.doi.org/10.1016/j.engstruct.2013.03.006

Yang, M. G.; Chen, Z. Q.; Hua, X.G. 2011. An Experimental Study on Using MR Damper to Mitigate Longitudinal Seismic Response of A Suspension Bridge, Soil Dynamics and Earthquake Engineering 31(8): 1171–1181. http://dx.doi.org/10.1016/j.soildyn.2011.04.006

Yang, M. G.; Chen, Z. Q.; Hua, X. G. 2010. A New Two-Node Catenary Cable Element for The Geometrically Non-linear Analysis of Cable-Supported Structures, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224(C6): 1173–1183. http://dx.doi.org/10.1243/09544062JMES1816




How to Cite

Yang, M.-G., Cai, C.-S., & Wei, B. (2015). A Combined Control Strategy for Vibration Mitigations of a Suspension Bridge Induced by Vehicle Braking Force. The Baltic Journal of Road and Bridge Engineering, 10(2), 118-125. https://doi.org/10.3846/bjrbe.2015.15