The dynamic parameters of passive human at temporary demountable grandstands during exposure to lateral vibration
Abstract
Modelling the interaction between crowds and temporary demountable grandstands with identifying the human dynamic properties are challenges for structure optimal design. In this paper, for investigating and understanding the human and structural lateral dynamic features. A demountable grandstand was tested to obtain its model parameters firstly. Then it is tested at amplitudes between 0.16 m/s2 to 1.54 m/s2 with 75 random waves through a shaking table when occupied by twenty persons. Afterword a simplified two-degree of freedom lumped dynamic model of the joint human-structure system is reinterpreted. Utilizing the state-space model, the passive crowd dynamic parameters are obtained, based on root mean square accumulation error analysis. Statistical analysis of the predictive results concludes that seated crowd model damping ratio is 0.5, and the probable natural frequency is 2.0 Hz with the model mass ratio 0.7. For standing crowd model, the probable natural frequency is 1.5 Hz with the model mass damping ratio 0.4, and the model mass ratio is 0.7. It may have ability to serve as a reference value that can be utilized in vibration safety and serviceability assessment of TDGs, to estimate realistically the vibration response on the occasions when crowd are seated or standing.
Keyword : human-structure interaction, temporary demountable grandstand, lateral vibration, experiment, passive crowd dynamic parameters, model analysis
How to Cite
Yuan, J., He, L., Fan, F., & Liu, C. (2018). The dynamic parameters of passive human at temporary demountable grandstands during exposure to lateral vibration. Journal of Civil Engineering and Management, 24(4), 265-283. https://doi.org/10.3846/jcem.2018.3073
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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BBC News. 2004. Religion show stand fall probed. Monday, 30 August [online], [cited 09 January 2018]. Available from Internet: http://news.bbc.co.uk
Bolton, A. 1992. Fatal mix caused stand fall, New Civil Engineer, 5–6.
Brito, V. L.; Pena, A. N.; Pimentel, R. L.; Brito, J. L. V. 2014. Modal tests and model updating for vibration analysis of temporary grandstand, Advances in Structural Engineering 17(5): 721–734. https://doi.org/10.1260/1369-4332.17.5.721
Brito, V. L.; Pimentel, R. L. 2009. Cases of collapse of demountable grandstands, Journal of Performance of Construction Facility 23(3): 151–159. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000006
Brito, V. L.; Pimentel, R. L. 2011. Finite element models for vibration analysis of temporary grandstands, in The 8th International Conference on Structural Dynamics (EURODYN), 2011, Leuven, Belgium, 957–963.
Busca, G.; Cappellini, A.; Manzoni, S.; Tarabini, M.; Vanali, M. 2014. Quantification of changes in modal parameters due to the presence of passive people on a slender structure, Journal of Sound and Vibration 333(21): 5641–5652. https://doi.org/10.1016/j.jsv.2014.06.003
Cappellini, A.; Manzoni, S.; Tarabini, M.; Vanali, M.; Cigada, A. 2016. Evaluation of the dynamic behaviour of steel staircases damped by the presence of people, Engineering Structures 115: 165–178. https://doi.org/10.1016/j.engstruct.2016.02.028
Crick, D.; Gilbert, Y. G. 2008. Monitoring and analysis of a temporary grandstand. Structural Engineering Report No. 275. Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada.
Dickie, J. F. 1983. Demountable grandstand, Structural Engineer 61(A3): 81–86.
Dickie, J. F.; Gibbs, S. 1991. Temporary seating assemblies, in: mobile and rapidly assembled structures, Topics in Engineering, Computational Mechanics Publications 8: 198.
Dickie, J. F.; Tomlinson, G. R. 1987. Static and dynamic considerations for demountable grandstands, in The International Conference on the Design and Construction of Non-Conventional Structure, 1987, London, UK,
Ellis, B. R.; Ji, T. 1997. Human-structure interaction in vertical vibration, Proceedings of Civil Engineers Structures and Buildings 122(1): 1–9. https://doi.org/10.1680/istbu.1997.29162
Fairley, T. E.; Griffin, M. J. 1990. The apparent mass of the seated human body in the fore-and-aft and lateral directions, Journal of Sound and Vibration 139(2): 299–306. https://doi.org/10.1016/0022-460X(90)90890-C
Foschi, R. O.; Gupta, A. 1987. Reliability of floors under impact vibration, Canadian Journal of Civil Engineering 14(5): 683–689. https://doi.org/10.1139/l87-098
Gibbs, S. 1990. Dynamic response of loosely jointed temporary grandstand seating: PhD thesis. University of Manchester, Manchester.
Greimann, L. F.; Klaiber, F. W. 1978. Dynamic forces induced by spectators, Journal of the Structural Division 104(ST2): 348–351.
Griffin, M. J. 1990. Handbook of human vibration. London: Academic Press.
Han, H. X.; Zhou, D.; Ji, T. 2017. Mechanical parameters of standing body and applications in human-structure interaction, International Journal of Applied Mechanics 9(2): 1750021. https://doi.org/10.1142/S1758825117500211
Harrison, R. E.; Yao, S.; Wright, J. R.; Reynolds, P. 2006. Humans bouncing on flexible structures–effect of structural properties, in The Conference Proceedings of the Society for Experimental Mechanics Series, IMAC-XXIV: Conference and Exposition on Structural Dynamic-Looking Forward: Technologies for IMAC, 2006, St. Louis, MI, United States.
Harrison, R. E.; Yao, S.; Wright, J. R.; Reynolds, P. 2008. Human jumping and bobbing forces on flexible structures: effect of structural properties, Journal of Engineering Mechanics 138(8): 663–675. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:8(663)
He, L.; Liu, C.; Wu, Z. Y. 2014. Parametric modeling and stability analysis of temporary grandstand, Applied Mechanics and Materials 578–579: 907–916. https://doi.org/10.4028/www.scientific.net/AMM.578-579.907
Holmlund, P.; Lundstrom, R. 1998. Mechanical impedance of the human body in the horizontal direction, Journal of Sound and Vibration 215(4): 801–812. https://doi.org/10.1006/jsvi.1998.1593
HSL. 2011. Identification of safety good practice in the construction and deconstruction of temporary demountable structures. Health and Safety Laboratory, Buxton, United Kingdom.
Ibrahim, Z. 2006. The effects of crowds on dynamic characteristics of stadia structures: PhD thesis. The University of Sheffield, Sheffield, UK.
Institution of Structural Engineers (IStructE). 2007. Temporary demountable structures – guidance on design, procurement and use. 3rd ed. London, United Kingdom.
Institution of Structural Engineers (IStructE). 2017. Temporary demountable structure – guidance on design, procurement and use. 4th ed. London, United Kingdom.
ISO 2631 Mechanical vibration and shock–evaluation of human exposure to whole-body vibration. Part 1: General requirement. International Organization for Standardization (ISO), 1997.
ISO 2631 Mechanical vibration and shock–evaluation of human exposure to whole-body vibration. Part 1: Vibration in buildings (1 Hz to 80 Hz). International Organization for Standardization (ISO), 2003.
Jalil, N. A. A. 2016. Mathematical model of the apparent mass of the back of a seated person exposed to fore-and-aft whole-body vibration, in The ICSV 2016-23rd International Congress on Sound and Vibration: From Ancient to Modern Acoustics, 2016, Athens, Greece.
Jesus, C. Oliveira, T.; Brito, V. L.; Pimentel, R. L. 2014. Influence of seated spectators on the transverse modal properties of temporary grandstands, in Proceedings of the 9th International Conference on Structural Dynamics, 2014, Portugal, Porto, 1013–1018.
Ji, T.; Ellis, B. R. 1997. Effective bracing systems for temporary grandstand, Structural Engineer 75(6): 95–100.
Ji, T.; Ellis, B. R.; Bell, A. J. 2003. Horizontal movements of frame structures induced by vertical loads, Proceedings of the Institution of Civil Engineers Structures & Buildings 156(SB2): 141–150. https://doi.org/10.1680/stbu.2003.156.2.141
Joint Working Group (JWG). 2008. Joint Working Group Dynamic performance requirements: recommendations for management, design and assessment. IStructE/DCLG/DCMS.
Jones, C. A.; Reynolds, P.; Pavic, A. 2011. Vibration serviceability of stadia structures subjected to dynamic crowd loads: A literature review, Journal of Sound and Vibration 330(8):1531–1566. https://doi.org/10.1016/j.jsv.2010.10.032
LABC MG0220812 Temporary demountable structures, technical guidance note. Local Authority Building Control in England and Wales, United Kingdom, 2012.
Lasowicz, N.; Jankowski, R. 2013. Numerical analysis of a temporary steel grandstand, in The Shell Structures: Theory and Applications – Proceedings of the 10th SSTA 2013 Conference, 2013, Gdansk, Poland, 3: 543–546.
Lasowicz, N.; Jankowski, R. 2015a. Application of polymer element in reduction of temporary steel grandstand vibrations, in The Advances in Mechanics: Theoretical, Computational and Interdisciplinary Isses-3rd Polish Congress of Mechanics, PCM 2015 and 21st International Conference on Computer Methods in Mechanics, 2015, Gdansk, Poland, 331–334.
Lasowicz, N.; Jankowski, R. 2016b. Experimental and numerical study on polymer element used for reduction of temporary steel grandstand vibrations, in The Recent Progress in Steel and Composite Structures – Proceedings of the 13th International Conference on Metal Structures, 2016, Zielona Gora, Poland, 215–222.
Lasowicz, N.; Jankowski, R. 2016a. The effectiveness of polymer damper in damage reduction of temporary steel grandstand, Key Engineering Materials 713: 171–174. https://doi.org/10.4028/www.scientific.net/KEM.713.171
Lasowicz, N.; Kwiecie, A.; Jankowski, R. 2015b. Experimental study on the effectiveness of polymer damper in damage reduction of temporary steel grandstand, in The 11th International Conference on Damage Assessment of Structures, 2015, Ghent, Belgium.
Lenzen, K. H. 1996. Vibration of steel joist-concrete slab floors, AISC Engineering Journal 3: 133–134.
Littler, J. D. 1996. Measuring the dynamic response of temporary grandstands, in Proceedings of Structural Dynamics (EURODYN 96), 1996, Florence, Italy.
Littler, J. D. 2002. Temporary demountable grandstands: dynamic response. Watford: Building Research Establishment.
Mansfield, N. J.; Lundstrom, R. 1999. The apparent mass of the human body exposed to non-orthogonal horizontal vibration, Journal of Biomechanics 32(12): 1269–1278. https://doi.org/10.1016/S0021-9290(99)00135-9
Marinho, I. J. P.; Vaz, L. E.; Pimentel, R. L. 2006. Optimization of temporary grandstands through finite element analysis, in The 17th International Congress of Mechanical Engineering, 2003, Sao Paulo, Brazil.
Matsumoto, Y.; Griffin, M. J. 2003. Mathematical model for the apparent masses of standing subjects exposed to vertical whole body vibration, Journal of Sound and Vibration 260(3): 431–451. https://doi.org/10.1016/S0022-460X(02)00941-0
Matsumoto, Y.; Griffin, M. J. 2011. The horizontal apparent mass of the standing human body, Journal of Sound and Vibration 330(13): 3284–3297. https://doi.org/10.1016/j.jsv.2011.01.030
MUTAmarq. 2013. Safe use and operation of temporary demountable fabric structures. London: Performance Textiles Association.
Nawayseh, N. 2015. Modelling of the vertical apparent mass at the seat surface and backrest, in The 29th Annual European Simulation and Modelling Conference, 2015, Leicester, UK, 278–283.
Nhleko, S. 2011. Human-induced lateral excitation of public assembly structures: PhD thesis. University of Oxford, Oxford.
Nhleko, S.; Blakeborough, A.; Williams, M. S.; Whittle, J. 2010. Dynamic testing of bracing patterns of a demountable grandstand, in The Conference on Structural Engineering, Mechanics and Computation, 2010, Cape Town, South Africa, 89–92.
Pernica, G. 1983. Dynamic live loads at a rock concert, Canadian Journal of Civil Engineering 10(2): 185–191. https://doi.org/10.1139/l83-034
Polensek, A. 1975. Damping capacity of nailed wood-joist floor, Wood Science 8(2): 141–151.
Rainer, J. H.; Pernica, G. 1981. Damping of a floor sample, in The Second Speciality Conference on Dynamic Response of Structures: Experimentation, Observation, Predication and Control, 1981, Atlanta, USA.
Reynolds, P.; Pavic, A.; Ibrahim, Z. 2004. Changes of modal properties of a stadium structure occupied by a crowd, in The 22nd International Modal Analysis Conference (IMACXXII), 2004, Dearborn, Michigan, USA.
Sachse, R.; Pavic, A.; Reynolds, P. 2002. The influence of a group of humans on modal properties of a structure, in The Proceedings of the 4th International Conference on Structural Dynamics, 2002, Munich, Germany.
Sachse, R.; Pavic, A.; Reynolds, P. 2003. Human-structure dynamic interaction in civil engineering dynamic: a literature review, Shock and Vibration Digest 35(1): 3–18. https://doi.org/10.1177/0583102403035001624
Sim, J. H. H. 2006. Human-structure interaction in cantilever stands: PhD thesis. The University of Oxford, Oxford.
Sim, J. H. H.; Blakeborough, A.; Williams, M. 2006. Modelling effects of passive crowds on grandstand vibration, Structures and Buildings 159(5): 261–272. https://doi.org/10.1680/stbu.2006.159.5.261
The MATHWORKS. 2010. MATLABR software.
Tuan, C. Y.; Saul, W. E. 1985. Loads due to spectator movements, Journal of Structural Engineering 111(2): 418–434. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:2(418)
Venuti, F.; Racic, V.; Corbetta, A. 2016. Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges, Journal of Sound and Vibration 379: 245–263. https://doi.org/10.1016/j.jsv.2016.05.047
Wei, L.; Griffin, M. J. 1998. Mathematical model for the apparent masses of the seated human body exposed to vertical vibration, Journal of Sound and Vibration 212(5): 855–874. https://doi.org/10.1006/jsvi.1997.1473
Yao, S.; Wright, J. R.; Pavic, A.; Reynolds, P. 2006. Experimental study of human induced dynamic forces due to jumping on a perceptibly moving structure, Journal of Sound and Vibration 296(1–2): 150–165. https://doi.org/10.1016/j.jsv.2006.02.018
Yuan, J.; He, L.; Fan, F.; Liu, C.; Zhang, K. 2014. Dynamic modeling and vibration analysis of temporary grandstand due to crowd-jumping loads, in The Proceedings of the 9th International Conference on Structural Dynamics, 2014, Portugal, Porto, 1051–1057.
Zhang, Z. F.; Hu, Z. Q.; Xu, Z. M.; He, Y. S.; Huang, S. R. 2016. A dynamic model of a seated human body based on dynamic response, Journal of Vibration and Shock 35(4): 104–109.
BBC News. 2004. Religion show stand fall probed. Monday, 30 August [online], [cited 09 January 2018]. Available from Internet: http://news.bbc.co.uk
Bolton, A. 1992. Fatal mix caused stand fall, New Civil Engineer, 5–6.
Brito, V. L.; Pena, A. N.; Pimentel, R. L.; Brito, J. L. V. 2014. Modal tests and model updating for vibration analysis of temporary grandstand, Advances in Structural Engineering 17(5): 721–734. https://doi.org/10.1260/1369-4332.17.5.721
Brito, V. L.; Pimentel, R. L. 2009. Cases of collapse of demountable grandstands, Journal of Performance of Construction Facility 23(3): 151–159. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000006
Brito, V. L.; Pimentel, R. L. 2011. Finite element models for vibration analysis of temporary grandstands, in The 8th International Conference on Structural Dynamics (EURODYN), 2011, Leuven, Belgium, 957–963.
Busca, G.; Cappellini, A.; Manzoni, S.; Tarabini, M.; Vanali, M. 2014. Quantification of changes in modal parameters due to the presence of passive people on a slender structure, Journal of Sound and Vibration 333(21): 5641–5652. https://doi.org/10.1016/j.jsv.2014.06.003
Cappellini, A.; Manzoni, S.; Tarabini, M.; Vanali, M.; Cigada, A. 2016. Evaluation of the dynamic behaviour of steel staircases damped by the presence of people, Engineering Structures 115: 165–178. https://doi.org/10.1016/j.engstruct.2016.02.028
Crick, D.; Gilbert, Y. G. 2008. Monitoring and analysis of a temporary grandstand. Structural Engineering Report No. 275. Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada.
Dickie, J. F. 1983. Demountable grandstand, Structural Engineer 61(A3): 81–86.
Dickie, J. F.; Gibbs, S. 1991. Temporary seating assemblies, in: mobile and rapidly assembled structures, Topics in Engineering, Computational Mechanics Publications 8: 198.
Dickie, J. F.; Tomlinson, G. R. 1987. Static and dynamic considerations for demountable grandstands, in The International Conference on the Design and Construction of Non-Conventional Structure, 1987, London, UK,
Ellis, B. R.; Ji, T. 1997. Human-structure interaction in vertical vibration, Proceedings of Civil Engineers Structures and Buildings 122(1): 1–9. https://doi.org/10.1680/istbu.1997.29162
Fairley, T. E.; Griffin, M. J. 1990. The apparent mass of the seated human body in the fore-and-aft and lateral directions, Journal of Sound and Vibration 139(2): 299–306. https://doi.org/10.1016/0022-460X(90)90890-C
Foschi, R. O.; Gupta, A. 1987. Reliability of floors under impact vibration, Canadian Journal of Civil Engineering 14(5): 683–689. https://doi.org/10.1139/l87-098
Gibbs, S. 1990. Dynamic response of loosely jointed temporary grandstand seating: PhD thesis. University of Manchester, Manchester.
Greimann, L. F.; Klaiber, F. W. 1978. Dynamic forces induced by spectators, Journal of the Structural Division 104(ST2): 348–351.
Griffin, M. J. 1990. Handbook of human vibration. London: Academic Press.
Han, H. X.; Zhou, D.; Ji, T. 2017. Mechanical parameters of standing body and applications in human-structure interaction, International Journal of Applied Mechanics 9(2): 1750021. https://doi.org/10.1142/S1758825117500211
Harrison, R. E.; Yao, S.; Wright, J. R.; Reynolds, P. 2006. Humans bouncing on flexible structures–effect of structural properties, in The Conference Proceedings of the Society for Experimental Mechanics Series, IMAC-XXIV: Conference and Exposition on Structural Dynamic-Looking Forward: Technologies for IMAC, 2006, St. Louis, MI, United States.
Harrison, R. E.; Yao, S.; Wright, J. R.; Reynolds, P. 2008. Human jumping and bobbing forces on flexible structures: effect of structural properties, Journal of Engineering Mechanics 138(8): 663–675. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:8(663)
He, L.; Liu, C.; Wu, Z. Y. 2014. Parametric modeling and stability analysis of temporary grandstand, Applied Mechanics and Materials 578–579: 907–916. https://doi.org/10.4028/www.scientific.net/AMM.578-579.907
Holmlund, P.; Lundstrom, R. 1998. Mechanical impedance of the human body in the horizontal direction, Journal of Sound and Vibration 215(4): 801–812. https://doi.org/10.1006/jsvi.1998.1593
HSL. 2011. Identification of safety good practice in the construction and deconstruction of temporary demountable structures. Health and Safety Laboratory, Buxton, United Kingdom.
Ibrahim, Z. 2006. The effects of crowds on dynamic characteristics of stadia structures: PhD thesis. The University of Sheffield, Sheffield, UK.
Institution of Structural Engineers (IStructE). 2007. Temporary demountable structures – guidance on design, procurement and use. 3rd ed. London, United Kingdom.
Institution of Structural Engineers (IStructE). 2017. Temporary demountable structure – guidance on design, procurement and use. 4th ed. London, United Kingdom.
ISO 2631 Mechanical vibration and shock–evaluation of human exposure to whole-body vibration. Part 1: General requirement. International Organization for Standardization (ISO), 1997.
ISO 2631 Mechanical vibration and shock–evaluation of human exposure to whole-body vibration. Part 1: Vibration in buildings (1 Hz to 80 Hz). International Organization for Standardization (ISO), 2003.
Jalil, N. A. A. 2016. Mathematical model of the apparent mass of the back of a seated person exposed to fore-and-aft whole-body vibration, in The ICSV 2016-23rd International Congress on Sound and Vibration: From Ancient to Modern Acoustics, 2016, Athens, Greece.
Jesus, C. Oliveira, T.; Brito, V. L.; Pimentel, R. L. 2014. Influence of seated spectators on the transverse modal properties of temporary grandstands, in Proceedings of the 9th International Conference on Structural Dynamics, 2014, Portugal, Porto, 1013–1018.
Ji, T.; Ellis, B. R. 1997. Effective bracing systems for temporary grandstand, Structural Engineer 75(6): 95–100.
Ji, T.; Ellis, B. R.; Bell, A. J. 2003. Horizontal movements of frame structures induced by vertical loads, Proceedings of the Institution of Civil Engineers Structures & Buildings 156(SB2): 141–150. https://doi.org/10.1680/stbu.2003.156.2.141
Joint Working Group (JWG). 2008. Joint Working Group Dynamic performance requirements: recommendations for management, design and assessment. IStructE/DCLG/DCMS.
Jones, C. A.; Reynolds, P.; Pavic, A. 2011. Vibration serviceability of stadia structures subjected to dynamic crowd loads: A literature review, Journal of Sound and Vibration 330(8):1531–1566. https://doi.org/10.1016/j.jsv.2010.10.032
LABC MG0220812 Temporary demountable structures, technical guidance note. Local Authority Building Control in England and Wales, United Kingdom, 2012.
Lasowicz, N.; Jankowski, R. 2013. Numerical analysis of a temporary steel grandstand, in The Shell Structures: Theory and Applications – Proceedings of the 10th SSTA 2013 Conference, 2013, Gdansk, Poland, 3: 543–546.
Lasowicz, N.; Jankowski, R. 2015a. Application of polymer element in reduction of temporary steel grandstand vibrations, in The Advances in Mechanics: Theoretical, Computational and Interdisciplinary Isses-3rd Polish Congress of Mechanics, PCM 2015 and 21st International Conference on Computer Methods in Mechanics, 2015, Gdansk, Poland, 331–334.
Lasowicz, N.; Jankowski, R. 2016b. Experimental and numerical study on polymer element used for reduction of temporary steel grandstand vibrations, in The Recent Progress in Steel and Composite Structures – Proceedings of the 13th International Conference on Metal Structures, 2016, Zielona Gora, Poland, 215–222.
Lasowicz, N.; Jankowski, R. 2016a. The effectiveness of polymer damper in damage reduction of temporary steel grandstand, Key Engineering Materials 713: 171–174. https://doi.org/10.4028/www.scientific.net/KEM.713.171
Lasowicz, N.; Kwiecie, A.; Jankowski, R. 2015b. Experimental study on the effectiveness of polymer damper in damage reduction of temporary steel grandstand, in The 11th International Conference on Damage Assessment of Structures, 2015, Ghent, Belgium.
Lenzen, K. H. 1996. Vibration of steel joist-concrete slab floors, AISC Engineering Journal 3: 133–134.
Littler, J. D. 1996. Measuring the dynamic response of temporary grandstands, in Proceedings of Structural Dynamics (EURODYN 96), 1996, Florence, Italy.
Littler, J. D. 2002. Temporary demountable grandstands: dynamic response. Watford: Building Research Establishment.
Mansfield, N. J.; Lundstrom, R. 1999. The apparent mass of the human body exposed to non-orthogonal horizontal vibration, Journal of Biomechanics 32(12): 1269–1278. https://doi.org/10.1016/S0021-9290(99)00135-9
Marinho, I. J. P.; Vaz, L. E.; Pimentel, R. L. 2006. Optimization of temporary grandstands through finite element analysis, in The 17th International Congress of Mechanical Engineering, 2003, Sao Paulo, Brazil.
Matsumoto, Y.; Griffin, M. J. 2003. Mathematical model for the apparent masses of standing subjects exposed to vertical whole body vibration, Journal of Sound and Vibration 260(3): 431–451. https://doi.org/10.1016/S0022-460X(02)00941-0
Matsumoto, Y.; Griffin, M. J. 2011. The horizontal apparent mass of the standing human body, Journal of Sound and Vibration 330(13): 3284–3297. https://doi.org/10.1016/j.jsv.2011.01.030
MUTAmarq. 2013. Safe use and operation of temporary demountable fabric structures. London: Performance Textiles Association.
Nawayseh, N. 2015. Modelling of the vertical apparent mass at the seat surface and backrest, in The 29th Annual European Simulation and Modelling Conference, 2015, Leicester, UK, 278–283.
Nhleko, S. 2011. Human-induced lateral excitation of public assembly structures: PhD thesis. University of Oxford, Oxford.
Nhleko, S.; Blakeborough, A.; Williams, M. S.; Whittle, J. 2010. Dynamic testing of bracing patterns of a demountable grandstand, in The Conference on Structural Engineering, Mechanics and Computation, 2010, Cape Town, South Africa, 89–92.
Pernica, G. 1983. Dynamic live loads at a rock concert, Canadian Journal of Civil Engineering 10(2): 185–191. https://doi.org/10.1139/l83-034
Polensek, A. 1975. Damping capacity of nailed wood-joist floor, Wood Science 8(2): 141–151.
Rainer, J. H.; Pernica, G. 1981. Damping of a floor sample, in The Second Speciality Conference on Dynamic Response of Structures: Experimentation, Observation, Predication and Control, 1981, Atlanta, USA.
Reynolds, P.; Pavic, A.; Ibrahim, Z. 2004. Changes of modal properties of a stadium structure occupied by a crowd, in The 22nd International Modal Analysis Conference (IMACXXII), 2004, Dearborn, Michigan, USA.
Sachse, R.; Pavic, A.; Reynolds, P. 2002. The influence of a group of humans on modal properties of a structure, in The Proceedings of the 4th International Conference on Structural Dynamics, 2002, Munich, Germany.
Sachse, R.; Pavic, A.; Reynolds, P. 2003. Human-structure dynamic interaction in civil engineering dynamic: a literature review, Shock and Vibration Digest 35(1): 3–18. https://doi.org/10.1177/0583102403035001624
Sim, J. H. H. 2006. Human-structure interaction in cantilever stands: PhD thesis. The University of Oxford, Oxford.
Sim, J. H. H.; Blakeborough, A.; Williams, M. 2006. Modelling effects of passive crowds on grandstand vibration, Structures and Buildings 159(5): 261–272. https://doi.org/10.1680/stbu.2006.159.5.261
The MATHWORKS. 2010. MATLABR software.
Tuan, C. Y.; Saul, W. E. 1985. Loads due to spectator movements, Journal of Structural Engineering 111(2): 418–434. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:2(418)
Venuti, F.; Racic, V.; Corbetta, A. 2016. Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges, Journal of Sound and Vibration 379: 245–263. https://doi.org/10.1016/j.jsv.2016.05.047
Wei, L.; Griffin, M. J. 1998. Mathematical model for the apparent masses of the seated human body exposed to vertical vibration, Journal of Sound and Vibration 212(5): 855–874. https://doi.org/10.1006/jsvi.1997.1473
Yao, S.; Wright, J. R.; Pavic, A.; Reynolds, P. 2006. Experimental study of human induced dynamic forces due to jumping on a perceptibly moving structure, Journal of Sound and Vibration 296(1–2): 150–165. https://doi.org/10.1016/j.jsv.2006.02.018
Yuan, J.; He, L.; Fan, F.; Liu, C.; Zhang, K. 2014. Dynamic modeling and vibration analysis of temporary grandstand due to crowd-jumping loads, in The Proceedings of the 9th International Conference on Structural Dynamics, 2014, Portugal, Porto, 1051–1057.
Zhang, Z. F.; Hu, Z. Q.; Xu, Z. M.; He, Y. S.; Huang, S. R. 2016. A dynamic model of a seated human body based on dynamic response, Journal of Vibration and Shock 35(4): 104–109.