Abstract
This paper suggests an approach to generate human jumping loads using wavelet decomposition and a database of individual jumping force records. A total of 1201 individual jumping force records of various frequencies were first collected. For each record, every single jumping impulse was extracted and decomposed by DB10 Wavelet into seven levels, and all the related decomposition information was stored into a database. The period of each jumping impulse in the same record was found to follow a normal distribution, and so does the contact ratio. In order to generate a jumping load time history having N impulses, Wavelet coefficients are first randomly selected from the database for different levels. They are then used to reconstruct N impulses by inverse wavelet transform. The periods and contract ratios are then randomly generated according to their probabilistic function. These parameters are assigned to each of the N impulses. The final jumping force time history is obtained by linking all the N impulses end to end. Examples are presented to show the simulation procedure. Due to the application of the Wavelet decomposition, the non-stationary features of the jumping load force in time-frequency domain can be preserved by the suggested simulation approach.
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References
Zivanovic, S., Pavic, A., Reynolds, P.: Vibration serviceability of footbridges under human-induced excitation: a literature review. J. Sound Vib. 279(1), 1–74 (2005)
Jones, C.A., Reynolds, P., Pavic, A.: Vibration serviceability of stadia structures subjected to dynamic crowd loads: a literature review. J. Sound Vib. 330(8), 1531–1566 (2011)
Rogers D.: Two more ‘wobbly’ stands. Construction news (2000)
Parker, D.: Rock fans uncover town hall floor faults. New Civ. Eng. 20, 1531–1566 (2003)
Erlingsson, S., Bodare, A.: Live load induced vibrations in Ullevi Stadium—dynamic dynamic soil analysis. Soil Dyn. Earthq. Eng. 15(3), 171–188 (1996)
de Brito, V.L., Pimentel, R.L.: Cases of collapse of demountable grandstands. J. Perform. Constr. Facil. 23, 151–159 (2009)
News. Gym workout caused Seoul building tremor. Bingtimes, (2011). http://epaper.jinghua.cn/html/2011-07/21/content_682126.htm
Wolmuth, B., Surtees, J.: Crowd-related failure of bridges. In: Proceedings of the ICE-Civil Engineering. Thomas Telford, 2003
Marhsall, R.D., Pfrang, E.O., Leyendecker, E.V., et al.: Investigation of the kansas city hyatt regency walkways collapse. US National Bureau of Standards (1982)
Dallard, P., Fitzpatrick, A.J., Flint, A., et al.: The London millennium footbridge. Struct. Eng. 79(22), 17–21 (2001)
Dallard, P., Fitzpatrick, T., Low, A., et al.: The Millennium Bridge, London: problems and solutions. Struct. Eng. 79(8), 15–17 (2001)
Fujino, Y., Pacheco, B.M., Nakamura, S.I., et al.: Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge. Earthq. Eng. Struct. Dyn. 22(9), 741–758 (1993)
Murray, T.M., Allen, D.E., Ungar, E.E.: Floor vibrations due to human activity (1997)
Bachmann, H., Pretlove, A.J., Rainer, J.H.: Dynamic forces from rhythmical human body motions (1991)
Ji, T., Ellis, B.R.: Floor vibration induced by dance-type loads: theory. Struct. Eng. 72(3/1), 37 (1994)
Brownjohn, J.M., Pavic, A., Omenzetter, P.: A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking. Can. J. Civ. Eng. 31(1), 65–77 (2004)
Bachmann, H., Ammann, W.: Vibrations in structures: induced by man and machines. Iabse (1987)
Ellis, B.R., Ji, T.: Loads generated by jumping crowds: numerical modelling. Struct. Eng. 82(17), 35–40 (2004)
Zivanovic, S., Pavić, A., Reynolds, P.: Probability-based prediction of multi-mode vibration response to walking excitation. Eng. Struct. 29(6), 942–954 (2007)
Racic, V., Pavic, A.: Mathematical model to generate near-periodic human jumping force signals. Mech. Syst. Signal Process. 24(1), 138–152 (2010)
Racic, V., Pavic, A.: Stochastic approach to modelling of near-periodic jumping loads. Mech. Syst. Signal Process. 24(8), 3037–3059 (2010)
Vidakovic, B.: Statistical Modeling by Wavelets. A Wiley-Interscience Publication, Hoboken (1999)
Hu, C.H., Li, G.H., Zhou, T.: System Analysis and Design Based on 7.x MATLAB- Wavelet Analysis. Third edition. Xi’an Electronic Science & Technology University Press, Xi’an (2003)
Jun, C., Ling, W., Bo, C., et al.: Dynamic properties of human jumping load and its modeling: experimental study. J. Vib. Eng. 27(1), 16–24 (2014)
Chen, J., Li, G., Lou, J., et al.: Acceleration response spectrum for predicting floor vibration subjected to occupants jumping. Eng. Struct. 43(7), 972–979 (2015)
Sim, J., Blakeborough, A., Williams, M.S., et al.: Statistical model of crowd jumping loads. J. Struct. Eng. 134(12), 1852–1861 (2008)
Massey Jr., F.J.: The Kolmogorov-Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46(253), 68–78 (1951)
Daubechies I.: Ten lectures on wavelets. SIAM (1992)
Cui, J.: An Introduction to Wavelets. Xi’an Jiaotong University Press, Xi’an (1995)
Walter, G.G.: A sampling theorem for wavelet subspaces. IEEE Trans. Inf. Theory 38(2), 881–884 (1992)
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Li, G., Chen, J. (2016). A Wavelet-Based Approach for Generating Individual Jumping Loads. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29763-7_19
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DOI: https://doi.org/10.1007/978-3-319-29763-7_19
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