Human-Induced Loads on Grandstands as Non-Stationary Gaussian Processes

Abstract:

In this contribution, we employ non-stationary filtered Gaussian processes as an enrichment of a periodic mean value in order to approximate crowd loads on grandstands. Our work generalizes previous considerations where the superposition of a mean value and a stationary filtered Gaussian noise was used, and helps therefore to better predict the response of a structure mainly in the transition stages. We specify general theory of stochastic differential equations within the context of grandstands by recalling particular moment equations, and demonstrate its benefits or drawbacks on two simple examples. Overall performance is measured in terms of the second moment evolutions in time and in terms of the total up-crossings of the system's response compared to previously developed stationary approximation and Monte Carlo simulation. Throughout, only an active part of a crowd is considered.

• Periodical: Applied Mechanics and Materials (Volume 837)
• Pages: 191-197
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.837.191
• Online since: June 2016
• Authors: Ondrej Rokos*, Jiří Maca
• Keywords: Crowd Load, Dynamic Analysis, Filtered Gaussian Noise, Grandstand, Random Forcing

References

[1] M. Verner, T. Plachy, M. Polak, An experiment focused on fans behavior and induced grandstand vibrations during a football match, submitted to Applied Mechanics and Materials (2015).

DOI: 10.4028/www.scientific.net/amm.837.75

[2] M. Verner, T. Plachy, M. Polak, An experimental study focused to spectators-induced vibrations of a cantilever grandstand during two sport matches, in: Proceedings of 53rd International Conference on Experimental Stress Analysis, 2015, CTU in Prague, Czech Republic, pp.73-78.

DOI: 10.4028/www.scientific.net/amm.827.312

[3] B.R. Ellis, T. Ji, Floor vibration induced by dance-type loads: verification, The Structural Engineer 72 (1994) 45-50.

[4] V. Racic, A. Pavic, Stochastic approach to modelling of near-periodic jumping loads, Mechanical Systems and Signal Processing 8 (2009) 3037-3059.

DOI: 10.1016/j.ymssp.2010.05.019

[5] V. Racic, A. Pavic, Mathematical model to generate near-periodic human jumping force signals, Mechanical Systems and Signal Processing 24 (2010) 138-152.

DOI: 10.1016/j.ymssp.2009.07.001

[6] J.H. Sim, Human structure interaction in cantilever grandstands, Ph.D. thesis, University of Oxford, (2006).

[7] M. Hermanussen, H. Danker-Hopfe, G.W. Weber, Body weight and the shape of the natural distribution of weight, in very large samples of German, Austrian and Norwegian conscripts, International Journal of Obesity 25 (2001) 1550-1553.

DOI: 10.1038/sj.ijo.0801715

[8] M. Grigoriu, Applied non-Gaussian processes: examples, theory, simulation, linear random vibrations and MATLAB solutions, Prentice Hall, (1995).

[9] M. Grigoriu, Stochastic calculus: applications in science and engineering, Birkhauser, (2002).

[10] T.T. Soong, M. Grigoriu, Random vibration of mechanical and structural systems, Prentice Hall, New Jersey, (1993).

[11] O. Rokos, Dynamic analysis of grandstands, Ph.D. thesis, CTU in Prague, (2014).

[12] G.G. Browning, Human perception of vibrations due to synchronized crowd loading in grandstands, Ph.D. thesis, University of Bath, (2011).

[13] ISO 2631-1: 1997, Mechanical vibration and shock – evaluation of human exposure to whole body vibration – part 1: general requirements, (1997).

DOI: 10.3403/30197820

[14] ISO 2631-2: 1997, Mechanical vibration and shock – evaluation of human exposure to whole body vibration – part 2: vibration in buildings (1 Hz to 80 Hz), (1997).

DOI: 10.3403/00050085

[15] O. Rokos, J. Maca, The response of grandstands driven by filtered Gaussian white noise processes, Advances in Engineering Software 72 (2014) 85-94.

DOI: 10.1016/j.advengsoft.2013.05.008

[16] P.J. Brockwell, R.A. Davis, Y. Yang, Continuous-time autoregression, Statistica Sinica 17 (2007) 63-80.

[17] J. Andel, Statistical analysis of time series, SNTL, 1976 (in Czech).

[18] O. Rokos, J. Maca, Stochastic approach in the human-induced vibration serviceability assessment of grandstands, in: Proceedings of IX International Conference on Structural Dynamics EURODYN, 2014, FEU do Porto, Portugal, pp.1019-1026.