Application of optimized spring–mass–damper pedestrian load models for vibration assessment of footbridges: numerical and experimental investigation of a cable-stayed system
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Abstract
Abstract This article explores the potential and accuracy of spring–mass–damper (SMD) pedestrian load modelling strategies for assessing human-induced vibrations of in-service footbridges. To this aim, a recent SMD modelling proposal based on uncoupled single-body measures (SMD-0, in the following) is specifically used for the calibration of key input parameters. Finite element numerical assumptions and findings are robustly supported by original experimental tests carried out on a case-study footbridge in Poland, proving that the proposed approach can serve as an effective tool for analysing vibrations in pedestrian systems. The research study, most importantly, integrates theoretical modelling with empirical and experimental validations, to enhance the credibility of the obtained results, as well as to support the general applicability of the presented methodology. Complex in-field tests are in fact conducted on the selected footbridge, aiming to assess the effects of pedestrians on its dynamic response. Numerical analyses, which are successively performed in ABAQUS/Standard, for a set of examined walking configurations, confirm the high sensitivity of the footbridge to resonance, which was also observed during the in-field tests. The presently used SMD-0 approach is further assessed towards past SMD literature proposals. As shown, the comparison of standard structural performance indicators (such as the peak acceleration value, root mean square and CREST factor) reveals a significant sensitivity of the footbridge response to the input parameters for the analyzed SMD models. Besides, the presently addressed SMD-0 model has the advantage of being based on single-body sensor measurements and its calibration is not affected by structural features. As such, potential applications of present findings could include the improvement of design standards and safety measures for similar structures.
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Research context
OpenAlex topics: Structural Engineering and Vibration Analysis · Railway Engineering and Dynamics · Structural Health Monitoring Techniques
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References (60)
Show source-provided references
1. Oviedo-Trespalacios O, Scott-Parker B. Footbridge usage in high-traffic flow highways: the intersection of safety and security in pedestrian decision-making. Transport Res F-Traf. 2017. https://doi.org/10.1016/j.trf.2017.06.010.10.1016/j.trf.2017.06.010 ↗
2. Bachmann H. ‘Lively’ footbridges – real challenge. Proc of Footbridge. 2002.
3. Caetano E, Cunha A. Dynamic Design of Slender Footbridges. Proc of ICSA. 2013.
4. Zhang B, Rasmussen B, Jorissen A, Harte A. Comparison of vibrational comfort assessment criteria for design of timber floors among the European countries. Eng Struct. 2013. https://doi.org/10.1016/j.engstruct.2013.03.028.10.1016/j.engstruct.2013.03.028 ↗
5. Feldmann M et al. Design of floor structures for human induced vibrations, JRC – ECCS joint report; 2009.
6. Wang L, He H, Li S. Structural vibration performance test based on smart phone and improved comfort evaluation method. Measurement. 2022. https://doi.org/10.1016/j.measurement.2022.111947.10.1016/j.measurement.2022.111947 ↗
7. Pańtak M. Elaboration of the vibration comfort criteria for footbridges during vibrations induced by pedestrians. Proc of IABMAS; 2012;2334–9.10.1201/b12352-350 ↗
8. Belykh I, Bocian M, Champneys AR, Daley K, Jeter R, Macdonald JHG, McRobbie A. Emergence of the London Millennium Bridge instability without synchronization. Nat Commun. 2021. https://doi.org/10.1038/s41467-021-27568-y.10.1038/s41467-021-27568-y ↗
9. Sánchez-Aparicio LJ, Ramos LF, Sena-Cruz L, Barros JO, Riveiro B. Experimental and numerical approaches for structural assessment in new footbridge designs (SFRSCC–GFPR hybrid structure). Compos Struct. 2015. https://doi.org/10.1016/j.compstruct.2015.07.041.10.1016/j.compstruct.2015.07.041 ↗
10. Bayat E, Milone A, Tubino F, Venuti F. Vibration serviceability assessment of a historic suspension footbridge. Buildings. 2022. https://doi.org/10.3390/buildings12060732.10.3390/buildings12060732 ↗
11. Moutinho C, Cunha A, Caetano E, Carvalho JM. Vibration control of a slender footbridge using passive and semiactive tuned mass dampers. Struct Control Health Monit. 2018. https://doi.org/10.1002/stc.2208.10.1002/stc.2208 ↗
12. Araújo MC Jr, Brito HMBF, Pimentel RL. Experimental evaluation of synchronization in footbridges due to crowd density. Struct Eng Int. 2009. https://doi.org/10.2749/101686609788957784.10.2749/101686609788957784 ↗
13. Bocian M, et al. Time-dependent spectral analysis of interactions within groups of walking pedestrians and vertical structural motion using wavelets. Mech Syst Signal Process. 2018. https://doi.org/10.1016/j.ymssp.2017.12.020.10.1016/j.ymssp.2017.12.020 ↗
14. Pirner M, Fischer O. Wind-induced vibrations of concrete stress-ribbon footbridges. J Wind Eng Ind Aerodyn. 1998. https://doi.org/10.1016/S0167-6105(98)00079-8.10.1016/S0167-6105(98)00079-8 ↗
15. Uyttersprot J, De Corte W, Ingelbinck B. Influence of SLS design requirements on the material consumption and self-weight of web-core sandwich panel FRP composite footbridges. Compos Struct. 2021. https://doi.org/10.1016/j.compstruct.2020.113334.10.1016/j.compstruct.2020.113334 ↗
16. Al-Rousan RZ, Al-Smadi YM, Laradhi AA. Operational modal analysis of the curved JUST footbridge induced by human. Procedia Manuf. 2020. https://doi.org/10.1016/j.promfg.2020.02.250.10.1016/j.promfg.2020.02.250 ↗
17. Drygala IJ, Dulinska JM. A theoretical and experimental evaluation of the modal properties of a cable-stayed footbridge. Procedia Eng. 2017. https://doi.org/10.1016/j.proeng.2017.09.347.10.1016/j.proeng.2017.09.347 ↗
18. Drygala IJ, Dulinska JM, Polak MA. Seismic assessment of footbridges under spatial variation of earthquake ground motion (SVEGM): experimental testing and finite element analyses. Sensors. 2020. https://doi.org/10.3390/s20041227.10.3390/s20041227 ↗
19. Zivanovic S, Pavic A, Reynolds P. Vibration serviceability of footbridges under human-induced excitation: a literature review. J Sound Vib. 2005. https://doi.org/10.1016/j.jsv.2004.01.019.10.1016/j.jsv.2004.01.019 ↗
20. Blanchard J, Davies BL, Smith JW. Design criteria and analysis for dynamic loading of footbridges, In: Proceedings of the DOE and DOT TRRL Symposium on Dynamic Behaviour of Bridges, Crowthorne, UK, May 19, 1977, pp. 90–106
21. Bachmann H, et al. Vibration problems in structures: practical guideline. Basel, Switzerland: Birkhäuser Verlag; 1995.10.1007/978-3-0348-9231-5 ↗
22. Bachmann H, Pretlove AJ, Rainer H. Dynamic forces from rhythmical human body motions. In Vibration Problems in Structures: Practical Guidelines; Birkhäuser: Basel, Switzerland, 1995; Appendix G.
23. Kerr SC, Bishop NWM. Human induced loading on flexible staircases. Eng Struct. 2001. https://doi.org/10.1016/S0141-0296(00)00020-1.10.1016/S0141-0296(00)00020-1 ↗
24. Pfeil PS, Varela WD, Costa NPA. Experimental calibration of a one degree of freedom biodynamic model to simulate human walking-structure interaction Eng. Struct. 2022. https://doi.org/10.1016/j.engstruct.2022.114330.10.1016/j.engstruct.2022.114330 ↗
25. Shahabpoor E, Pavic A, Racic V. Interaction between walking humans and structures in vertical direction: a literature review. Shock Vib. 2016. https://doi.org/10.1155/2016/3430285.10.1155/2016/3430285 ↗
26. Rezende FA, Brunet O Jr, Lopes Carvalho EM, Varela WD, Pereira AMB. Vibration-based sensitivity analysis of a flexible steel footbridge using probabilistic walking models. Eng Struct. 2024. https://doi.org/10.1016/j.engstruct.2023.117343.10.1016/j.engstruct.2023.117343 ↗
27. Brunet O Jr, Rezende F, Carvalho EML, Varela WD, Pereira AMB. Probabilistic vibration performance assessment of a long-span steel footbridge. J Perform Constr Facil. 2022. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001688.10.1061/(ASCE)CF.1943-5509.0001688 ↗
28. Rezende F, Brunet O Jr, Varela WD, Pereira A, Carvalho E. Evaluation of TMD performance in footbridges using human walking probabilistic models. Vibration. 2021. https://doi.org/10.3390/vibration4020021.10.3390/vibration4020021 ↗
29. Bedon C, Santos FA. Effect of spring-mass-damper pedestrian models on the performance of low-frequency or lightweight glazed floors. App Sci. 2023. https://doi.org/10.3390/app13064023.10.3390/app13064023 ↗
30. Koopman B, Grootenboer HJ, de Jongh HJ. An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking. J Biomech. 1995. https://doi.org/10.1016/0021-9290(94)00185-7.10.1016/0021-9290(94)00185-7 ↗
31. Brownjohn JMW, Chen J, Bocian M, Racic V, Shahabpoor E. Using inertial measurement units to identify medio-lateral ground reaction forces due to walking and swaying. J Sound Vib. 2018. https://doi.org/10.1016/j.jsv.2018.04.019.10.1016/j.jsv.2018.04.019 ↗
32. Bocian M, Macdonald J, Burn J, Redmill D. Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment. Eng Struct. 2015. https://doi.org/10.1016/j.engstruct.2015.09.043.10.1016/j.engstruct.2015.09.043 ↗
33. Bocian M, Macdonald JHG, Burn JF. Biomechanically inspired modeling of pedestrian-induced vertical self-excited forces. J Bridge Eng. 2013. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000490.10.1061/(ASCE)BE.1943-5592.0000490 ↗
34. Geyer H, Seyfarth A, Blickhan R. Compliant leg behaviour explains basic dynamics of walking and running. Proc R Soc Biol Sci. 2006. https://doi.org/10.1098/rspb.2006.3637.10.1098/rspb.2006.3637 ↗
35. White RE, Alexander NA, Macdonald JHG, Bocian M. Characterisation of crowd lateral dynamic forcing from full-scale measurements on the Clifton Suspension Bridge. Structures. 2020. https://doi.org/10.1016/j.istruc.2019.11.012.10.1016/j.istruc.2019.11.012 ↗
36. Wang L, Nagarajaiah S, Shi W, Zhou Y. Semi-active control of walking-induced vibrations in bridges using adaptive tuned mass damper considering human-structure-interaction. Eng Struct. 2021. https://doi.org/10.1016/j.engstruct.2021.112743.10.1016/j.engstruct.2021.112743 ↗
37. Wang L, Zhou Y, Shi W. Random crowd-induced vibration in footbridge and adaptive control using semi-active TMD including crowd-structure interaction. Eng Struct. 2024. https://doi.org/10.1016/j.engstruct.2024.117839.10.1016/j.engstruct.2024.117839 ↗
38. Bedon C. Single body sensor for calibration of Spring-Mass-Damper parameters in biodynamic pedestrian modelling. Measurement. 2023. https://doi.org/10.1016/j.measurement.2023.113258.10.1016/j.measurement.2023.113258 ↗
39. Galbraith FW, Barton MV. Ground loading from footsteps. JASA. 1970;48(5):1288–92.10.1121/1.1912271 ↗
40. ISO 10137:2007(E) - Bases for design of structures - Serviceability of buildings and walkways against vibrations
41. SÉTRA 2006: Assessment of Vibrational Behaviour of Footbridges under Pedestrian Loading. Technical Guide; Technical Department for Transport, Roads and Bridges Engineering and Road Safety: Paris, France, 2006
42. Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges, (CEN, 2003)
43. BS NA EN 1991–2: UK National Annex to Eurocode 1. Actions on structures. Traffic loads on bridges. British Standards Institution.
44. Miyamori Y, Obata T, Hayashikawa T, Sato K. 2001. Study on identification of human walking model based on dynamic response characteristics of pedestrian bridges. In Proceedings of the Eighth East Asia-Pacific Conference on Structural Engineering and Construction, Paper No. 1066
45. Kim SH, Cho KI, Choi MS, Lim JY. Development of human body model for the dynamic analysis of footbridges under pedestrian induced excitation. Steel Struct. 2008;8:333–45.
46. ISO 5982.
47. Caprani CC, Keogh J, Archbold P, Fanning P. Characteristic vertical response of a footbridge due to crowd loading. In: EURODYN 2011 Proceedings of the 8th International Conference on Structural Dynamics, Leuven, Belgium. pp. 978–985.
48. Silva FT, Brito HMBF, Pimentel RL. Modelling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges. Can J Civil Eng. 2013. https://doi.org/10.1139/cjce-2011-0587.10.1139/cjce-2011-0587 ↗
49. Toso MA, Gomes HM, da Silva FT, Pimentel RL. Experimentally fitted biodynamic models for pedestrian-structure interaction in walking situations. Mech Syst Signal Process. 2016. https://doi.org/10.1016/j.ymssp.2015.10.029.10.1016/j.ymssp.2015.10.029 ↗
50. Racic W, Pavic A, Brownjohn JMW. Experimental identification and analytical modelling of human walking forces: literature review. J Sound Vib. 2009. https://doi.org/10.1016/j.jsv.2009.04.020.10.1016/j.jsv.2009.04.020 ↗
51. Wang H, Chen J, Brownjohn JMW. Parameter identification of pedestrian’s spring-mass-damper model by ground reaction force records through a particle filter approach. J Sound Vib. 2017. https://doi.org/10.1016/j.jsv.2017.09.020.10.1016/j.jsv.2017.09.020 ↗
52. Ye XW, Dong CZ, Liu T. A review of machine vision-based structural health monitoring: methodologies and applications. J Sens. 2016. https://doi.org/10.1155/2016/71030-39.10.1155/2016/71030-39 ↗
53. Bocian M, Nikitas N, Kalybek M, et al. Dynamic performance verification of the Rędziński Bridge using portable camera-based vibration monitoring systems. Archiv Civ Mech Eng. 2023. https://doi.org/10.1007/s43452-022-00582-7.10.1007/s43452-022-00582-7 ↗
54. Rothberg SJ at al., An international review of laser Doppler vibrometry: Making light work of vibration measurement, Opt. Laser Eng. 2017; https://doi.org/10.1016/j.optlaseng.2016.10.02310.1016/j.optlaseng.2016.10.023 ↗
55. Pakos W at al., Experimental research of cable tension tuning of a scaled model of cable stayed bridge, Arch.Civ.Mech.Eng. 2016; https://doi.org/10.1016/j.acme.2015.09.00110.1016/j.acme.2015.09.001 ↗
56. The LMS Test.Lab Modal Analysis manual LMS Test.Lab
57. Ewins DJ. Modal testing: theory, practise and application. 2nd ed. Philadelphia, PA, USA: Research Studies Press Ltd.; 2000.
58. Benedettini F, Gentile C. Operational modal testing and FE model tuning of a cable-stayed bridge. Eng Struct. 2011. https://doi.org/10.1016/j.engstruct.2011.02.046.10.1016/j.engstruct.2011.02.046 ↗
59. Thomson W. Theory of Vibration with Applications. 4th ed. CRC Press; 2018.10.1201/9780203718841 ↗
60. Simulia ABAQUS. 2013. Users’ Manual Version 6.13 Documentation; Dassault Systemes: Velizy-Villacoublay, France, 2015