, Volume 50, Issue 3, pp 809–824 | Cite as

Tuned Mass Damper optimization for the mitigation of human-induced vibrations of pedestrian bridges

  • Federica Tubino
  • Giuseppe Piccardo
Advances in Dynamics, Stability and Control of Mechanical Systems


The design of Tuned Mass Dampers (TMD) to satisfy serviceability requirements is becoming more and more usual in the current design of footbridges. This paper analyzes the TMD design for the mitigation of pedestrian-induced vibrations with three main objectives: the introduction of a specific TMD optimization criterion for pedestrian-induced vibrations of footbridges, a critical analysis of the applicability to this specific loading scenario of classic literature optimization criteria, and a quantification of the TMD efficiency in the reduction of the footbridge acceleration. A numerical optimization criterion is proposed, based on the maximization of an efficiency factor, defined as the ratio between the uncontrolled acceleration standard deviation and the controlled one. Optimum TMD parameters are compared with classic criteria given by the literature. A possible modification of TMD parameters that permits to keep the TMD relative displacement within prescribed limits (aspect that is often a technical requirement in the TMD design) is also discussed. Monte Carlo simulations are carried out in order to confirm the validity of the standard deviation-based optimization for the reduction of the maximum dynamic response of the bridge. An application to a real footbridge is finally presented.


Footbridges Human-induced vibrations Optimization Serviceability Tuned Mass Damper Vibration Control 



This work has been partially supported by the Italian Ministry of Education, Universities and Research (MIUR, PRIN co-financed program “Dynamics, Stability and Control of Flexible Structures”) and by University of Genoa (Progetto di Ateneo 2012 “Dinamica e stabilità di strutture flessibili”).


  1. 1.
    Zivanovic S, Pavic A, Reynolds P (2005) Vibration serviceability of footbridges under human-induced excitation: a literature review. J Sound Vib 279:1–74ADSCrossRefGoogle Scholar
  2. 2.
    Zivanovic S (2012) Benchmark footbridge for vibration serviceability assessment under vertical component of pedestrian load. J Struct Eng ASCE 138(10):1192–1202Google Scholar
  3. 3.
    Zivanović S, Pavić A, Ingólfsson ET (2010) Modeling spatially unrestricted pedestrian traffic on footbridges. J Struct Eng ASCE 136(10):1296–1308CrossRefGoogle Scholar
  4. 4.
    Van Nimmen K, Lombaert G, De Roeck G, Van den Broeck P (2014) Vibration serviceability of footbridges: evaluation of the current codes of practice. Eng Struct 59:448–461CrossRefGoogle Scholar
  5. 5.
    SETRA (2006) Footbridges. Assessment of vibrational behaviour of footbridges under pedestrian loading, Technical Guide. Technical Department for Transport, Roads and Bridges Engineering and Road Safety (SETRA), Ministry of Transport, Republique FrancaiseGoogle Scholar
  6. 6.
    Brownjohn J, Fok P, Roche M, Omenzetter P (2004) Long span steel pedestrian bridge at Singapore Changi Airport—Part 2: crowd loading tests and vibration mitigation measures. Struct Eng 82(16):28–34Google Scholar
  7. 7.
    Bonelli A, Bonora M, Bursi O, Santini S, Vulcan L, Zasso A (2008) Dynamic analysis and vibration control of the twin deck curved suspension foot/cycle bridge “Ponte del Mare”. In: Proceedings footbridge 2008 conference, PortoGoogle Scholar
  8. 8.
    Caetano E, Cunha A, Moutinho C, Magalhães F (2010) Studies for controlling human-induced vibration of the Pedro e Inês footbridge, Portugal. Part 2: implementation of tuned mass dampers. Eng Struct 32:1082–1091CrossRefGoogle Scholar
  9. 9.
    Soong TT, Dargush GF (1997) Passive energy dissipation systems in structural engineering. Wiley, ChichesterGoogle Scholar
  10. 10.
    GERB (2000) Vibration Isolation Systems, Edition 2000Google Scholar
  11. 11.
    Warburton GB (1982) Optimum adsorber parameters for various combinations of response and excitation parameters. Earthq Eng Struct Dynam 10:381–401CrossRefGoogle Scholar
  12. 12.
    Krenk S (2005) Frequency analysis of the Tuned Mass Damper. J Appli Mech Trans ASME 72:936–942CrossRefMATHGoogle Scholar
  13. 13.
    Fujino Y, Abè M (1993) Design formulas for tuned mass dampers based on a perturbation technique. Earthq Eng Struct Dyn 22:833–854CrossRefGoogle Scholar
  14. 14.
    Gattulli V, Di Fabio F, Luongo A (2001) Simple and double Hopf bifurcations in aeroelastic oscillators with tuned mass dampers. J Franklin Inst 338(2–3):187–201CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Bisegna P, Caruso G (2012) Closed-form formulas for the optimal pole-based design of tuned mass dampers. J Sound Vib 331:2291–2314ADSCrossRefGoogle Scholar
  16. 16.
    Hoang N, Fujino Y, Warnitchai P (2008) Optimal tuned mass damper for seismic applications and practical design formulas. Eng Struct 30:707–715CrossRefGoogle Scholar
  17. 17.
    Marano GC, Greco R, Chiaia B (2010) A comparison between different optimization criteria for tuned mass dampers design. J Sound Vib 329:4880–4890ADSCrossRefGoogle Scholar
  18. 18.
    Piccardo G, Tubino F (2012) Equivalent spectral model and maximum dynamic response for the serviceability analysis of footbridges. Eng Struct 40:445–456CrossRefGoogle Scholar
  19. 19.
    ISO10137 (2007) Bases for design of structures—serviceability of buildings and walkways against vibration. International Organization for Standardization, GenevaGoogle Scholar
  20. 20.
    BSI (2008) UK National Annex to Eurocode 1: actions on structures—Part 2: Traffic loads on bridges. NA to BS EN 1991-2:2003, British Standards InstitutionGoogle Scholar
  21. 21.
    Piccardo G, Tubino F (2012) Dynamic response of Euler- Bernoulli beams to resonant harmonic moving loads. Struct Eng Mech 44(5):681–704CrossRefGoogle Scholar
  22. 22.
    Piccardo G, Tubino F (2009) Simplified procedures for the vibration serviceability analysis of footbridges subjected to realistic walking loads. Comput Struct 87:890–903CrossRefGoogle Scholar
  23. 23.
    Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2014) Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes. Int J Non-Linear Mech 63:19–30CrossRefGoogle Scholar
  24. 24.
    Di Matteo A, Lo Iacono F, Navarra G, Pirrotta A (2014) Optimal tuning of TLCD systems in random vibrations by means of an approximate formulation. Meccanica (Submitted)Google Scholar
  25. 25.
    Vintani A, Spinelli F, Tavecchio C, Solari G, Carassale L, Tubino F (2011) Lighter structures. Design and check of behavior by testing. In: Proceedings IABSE-IASS Symposium, LondonGoogle Scholar
  26. 26.
    Lamarque C-H, Ture Savadkoohi A, Dimitrijevic Z (2014) Dynamics of a linear system with time-dependent mass and a coupled light mass with non-smooth potential. Meccanica 49:135–145CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Porfiri M, dell’Isola F, Santini E (2005) Modeling and design of passive electric networks interconnecting piezoelectric transducers for distributed vibration control. Int J Appl Electromagn Mech 21(2):69–87Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.DICCA - University of GenoaGenoaItaly

Personalised recommendations