Optimization and application of multiple tuned mass dampers in the vibration control of pedestrian bridges

  • Lu, Zheng (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Chen, Xiaoyi (Research Institute of Structural Engineering and Disaster Reduction, Tongji University) ;
  • Li, Xiaowei (Research Institute of Structural Engineering and Disaster Reduction, Tongji University) ;
  • Li, Peizhen (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University)
  • Received : 2014.10.09
  • Accepted : 2017.01.05
  • Published : 2017.04.10


An effective design approach for Multiple Tuned Mass Dampers (MTMDs) in pedestrian bridges was proposed by utilizing the transfer function to obtain each TMD's optimum stiffness and damping. A systematic simulation of pedestrian excitations was described. The motion equation of a typical MTMD system attached to a Multi-degree-of-freedom (MDOF) system was presented, and the transfer function from the input pedestrian excitations to the output acceleration responses was defined. By solving the minimum norm of the transfer function, the parameters of the MTMD which resulted in the minimum overall responses can be obtained. Two applications of lightly damped pedestrian bridges attached with MTMD showed that MTMDs designed through this method can significantly reduce the structural responses when subjected to pedestrian excitations, and the vibration control effects were better than the MTMD when it was considered as being composed of equal number and mass ratios of TMDs designed by classical Den Hartog method.


Supported by : National Natural Science Foundation of China


  1. Abubakar, I.M. and Farid, B.J.M. (2009), "Generalized Den Hartog tuned mass damper system for control of vibrations in structures", Seismic Control ., 59, 185-193.
  2. Allen, D.E. and Murray, T.M. (1993), "Design criterion for vibrations due to walking", AISC Eng. J., 30(4), 117-129.
  3. Anh, N.D. and Nguyen, N.X. (2012), "Extension of equivelent linearization method to design of TMD for linear damped systems", Struct. Control. Hlth., 19(6), 565-573.
  4. British Standard 5400 (2006), Specification for Loads, Steel, concrete and composite bridges.
  5. Carpineto, N., Lacarbonara, W. and Vestroni, F. (2010), "Mitigation of pedestrian-induced vibrations in suspension footbridges via multiple tuned mass dampers", J. Vib. Control., 16(5), 749-776.
  6. Chakraborty, S. and Debbarma, R. (2016), "Robust optimum design of tuned liquid column damper in seismic vibration control of structures under certain bounded system parameters", Struct. Infrastr. Eng., 12(5), 592-602.
  7. Chen, X., Ding, Y.L., Li, A.Q., Zhang, Z.Q. and Sun, P. (2012). "Investigations on serviceability control of long-span structures under human-induced excitation", Earthq. Eng. Struct. D., 11(1), 57-71.
  8. Chinese Code CJJ69 (1995), Technical Specifications of Urban Pedestrian Overcrossing and Underpass, Beijing.
  9. Da Silva, J.G.S., Vellasco, P.C.G., De Andrade, S.A.L., Soeiro, F.J.D.C.P. and Werneck, R.N. (2003). "An evaluation of the dynamical performance of composite slabs", Comput. Struct., 81(1), 1905-1913.
  10. Dai, K.S., Wang, J.Z., Mao, R.F., Lu, Z. and Chen, S.E. (2016), "Experimental investigation on dynamic characterization and seismic control performance of a TLPD system", Struct. Des. Tall Spec. Build., DOI: 10.1002/tal.1350.
  11. Fujino, Y., Pacheco, B.M., Nakamura, S. and Warnitchai, P. (1993), "Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge", Earthq. Eng. Struct. D., 22(9), 741-785.
  12. Gong, S.M. and Zhou, Y. (2016), "Experimental study and numerical simulation on a new type of viscoelastic damper with strong nonlinear characteristics", Struct. Control. Hlth, DOI: 10.1002/stc.1897.
  13. Iba, D., Masuda, A. and Sone, A. (2006), "Robust design method of multi-degree-of-freedom passive tuned mass damper by control theory", ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference, Vancouver, BC, Canada, July.
  14. Li, C.X. (2002), "Optimum multiple tuned mass dampers for structures under the ground acceleration based on DDMF and ADMF", Earthq. Eng. Struct. D., 31, 897-919.
  15. Li, Q., Fan, J.S., Nie, J.G., Li, Q.W. and Chen, Y. (2010), "Crowd-induced random vibration of footbridge and vibration control using multiple tuned mass dampers", J. Sound. Vib., 329(19), 4068-4092.
  16. Lu, X.L., Ding, K., Shi, W.X. and Weng, D.G. (2012), "Tuned mass dampers for human-induced vibration control of the Expo Culture Centre at the World Expo 2010 in Shanghai, China", Struct. Eng. Mech., 43(5), 607-621.
  17. Lu, Z., Chen, X.Y., Lu, X.L. and Yang, Z. (2016b), "Shaking table test and numerical simulation of an RC frame-core tube structure for earthquake-induced collapse", Earthq. Eng. Struct. D., 45(9), 1537-1556.
  18. Lu, Z., Chen, X.Y., Zhang, D.C. and Dai, K.S. (2016a), "Experimental and analytical study on the performance of particle tuned mass dampers under seismic excitation", Earthq. Eng. Struct. D., DOI: 10.1002/eqe.2826.
  19. Lu, Z., Lu, X.L, Jiang H.J. and Masri, S.F. (2014), "Discrete element method simulation and experimental validation of particle damper system", Eng. Comput, 31(4):810-823.
  20. Lu, Z., Lu, X.L, Lu, W.S. and Masri, S.F. (2012), "Shaking table test of the effects of multi-unit particle dampers attached to an MDOF system under earthquake excitation", Earthq. Eng. Struct. D., 41(5), 987-1000.
  21. Lu, Z., Lu, X.L. and Masri, S.F. (2010), "Studies of the performance of particle dampers under dynamic loads", J. Sound Vib., 329(26):5415-5433.
  22. Lu, Z., Wang, D.C. and Zhou, Y. (2017a), "Experimental parametric study on wind-induced vibration control of particle tuned mass damper on a benchmark high-rise building", Struct. Des. Tall Spec., DOI: 10.1002/tal.1359
  23. Lu, Z., Wang, D.C., Masri, S.F. and Lu, X.L. (2016c), "An experimental study of vibration control of wind-excited highrise buildings using particle tuned mass dampers", Smart. Struct. Syst., 18(1), 93-115.
  24. Lu, Z., Yang, Y.L., Lu, X.L. and Liu, C.Q. (2017b), "Preliminary study on the damping effect of a lateral damping buffer under a debris flow load", Appl. Sci., 7(2), 201.
  25. Marano, G.C., Sgobba, S., Greco, R. and Mezzina, M. (2008), "Robust optimum design of tuned mass dampers devices in random vibrations mitigation", J. Sound. Vib., 313(3), 472-492.
  26. Masaki, N. and Hirata, H. (2004),"Vibration control performance of damping coupled tuned mass dampers", ASME/JSME 2004 Pressure Vessels and Piping Conference, San Diego, California, July.
  27. Miguel, L.F.F, Lopez, R.H., Miguel, L.F.F. and Torri, A.J. (2016), "A novel apporach to the optimum design of MTMDs under seismic excitations", Earthq. Eng. Struct. D., DOI: 10.1002/stc.1845.
  28. Mrabet, E., Guedri, M., Ichchou, M. and Ghanmi, S. (2015), "New approaches in reliability based optimization of tuned mass damper in presence of uncertain bounded parameters", J. Sound Vib., 355, 93-116.
  29. Rana, R. and Soong, T.T. (1998), "Parametric study and simplified design of tuned mass dampers", Eng. Struct., 20(3), 193-204.
  30. Salvi, J. and Rizzi, E. (2015), "Optimum tuning of tuned mass dampers for frame structures under earthquake excitation", Struct. Control. Hlth., 22(4), 707-725.
  31. Singh, M.P., Singh, S. and Moreschi, L.M. (2002), "Tuned mass dampers for response control of torsional buildings", Earthq. Eng. Struct. D., 31, 749-769.
  32. Tubino, F. and Piccardo, G. (2015), "Tuned mass damper optimization for the mitigation of human-induced vibrations of pedestrian bridges", Meccanica, 50(3), 809-824.
  33. Wong, K.K.F. and Johnson, J. (2009), "Seismic energy dissipation of inelastic structures with multiple tuned mass dampers", J. Eng. Mech., 135(4), 265-275.
  34. Xiang, P. and Nishitani, A. (2015), "Optimum design and application of non-traditional tuned mass damper toward seismic response control with experimental verification", Earthq. Eng. Struct. D., 44(13), 2199-2220.
  35. Xu, K. and Igusa, T. (1992). "Dynamic characteristics of multiple substructures with closely spaced frequencies", Earthq. Eng. Struct. D., 21(12), 1059-1070.
  36. Yang, F., Sedaghati, R. and Esmailzadeh, E. (2010), "Vibration suppression using distributed tuned mass damper", Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Montreal, Quebec, Canada, August.
  37. Yang, Y.Q. and Ke, Z.T. (2008), "Vibration control of footbridge", Constr. Des. Project, 2, 93-97.
  38. Zhou, Y., Zhang, C.Q. and Lu, X.L. (2016), "Seismic performance of a damping outrigger system for tall buildings", Struct. Control. Hlth., DOI: 10.1002/stc.1864.

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