Structural Engineering and Mechanics

  • 제86권2호
  • /
  • Pages.237-247
  • /
  • 2023
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A spectral model for human bouncing loads

  • Jiecheng Xiong (School of Civil Engineering, Zhengzhou University) ;
  • Jun Chen (College of Civil Engineering, Tongji University)
  • 투고 : 2021.05.14
  • 심사 : 2023.03.21
  • 발행 : 2023.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

Fourier series-based models in the time domain are frequently established to represent individual bouncing loads, which neglects the stochastic property of human bouncing activity. A power spectral density (PSD) model in the frequency domain for individual bouncing loads is developed herein. An experiment was conducted on individual bouncing loads, resulting in 957 records linked to form long samples to achieve a fine frequency resolution. The Welch method was applied to the linked samples to obtain the experimental PSD, which was normalized by the bouncing frequency and the harmonic order. The energy, energy distribution center, and energy distribution shape of the experimental PSD were investigated to establish the PSD model. The proposed model was used to analyze structural vibration responses using stochastic vibration theory, which was verified via field measurements. It is believed that this framework can evaluate the vibration capacity of structures excited by bouncing crowds, such as concert halls and grandstands.

키워드

과제정보

This work was supported by the National Natural Science Foundation of China (Grant number: 52008376, 52178151) and the Key Scientific Research Project of Colleges and Universities in Henan Province (Grant number: 21A560014)

참고문헌

  1. Bassoli, E., Van Nimmen, K., Vincenzi, L. and Van den Broeck, P. (2018), "A spectral load model for pedestrian excitation including vertical human-structure interaction", Eng. Struct., 156, 537-547. https://doi.org/10.1016/j.engstruct.2017.11.050.
  2. Bendat, J.S. and Piersol, A.G. (2011), Random Data Analysis and Measurement Procedures, 4th Edition, John Wiley & Sons, Hoboken, New Jersey, USA.
  3. Berardengo, M., Drago, L., Manzoni, S. and Vanali, M. (2019), "An approach to predict human-structure interaction in the case of staircases", Arch. Appl. Mech., 89(10), 2167-2191. https://doi.org/10.1007/s00419-019-01569-2.
  4. Brownjohn, J.M.W., Pavic, A. and Omenzetter, P. (2004), "A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking", Can. J. Civil Eng., 31(1), 65-77. https://doi.org/10.1139/l03-072.
  5. Cao, L. and Chen, Y.F. (2020), "A simplified method for determining the acceleration amplitudes of long-span floor system under walking/running loads", Struct. Eng. Mech., 75(3), 377-387. http://doi.org/10.12989/sem.2020.75.3.377.
  6. Cao, L., Liu, J., Zhou, X. and Chen, Y.F. (2018), "Vibration performance characteristics of a long-span and light-weight concrete floor under human-induced loads", Struct. Eng. Mech., 65(3), 349-357. https://doi.org/10.12989/sem.2018.65.3.349.
  7. Caprani, C. (2014), "Application of the pseudo-excitation method to assessment of walking variability on footbridge vibration", Comput. Struct., 132, 43-54. https://doi.org/10.1016/j.compstruc.2013.11.001.
  8. Chen, J., Li, G. and Racic, V. (2018a), "A data-driven wavelet-based approach for generating jumping loads", Mech. Syst. Signal Pr., 106, 49-61. https://doi.org/10.1016/j.ymssp.2017.12.013.
  9. Chen, J., Tan, H., Van Nimmen, K. and Van den Broeck, P. (2019), "Data-driven synchronization analysis of a bouncing crowd", Shock Vib., 2019, Article ID 8528763. https://doi.org/10.1155/2019/8528763.
  10. Chen, J., Wang, J. and Brownjohn, J.M.W. (2018b), "Power spectral-density model for pedestrian walking load", J. Struct. Eng., 145(2), 4018239. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002248.
  11. Chen, J., Wang, L., Racic, V. and Lou, J. (2016), "Acceleration response spectrum for prediction of structural vibration due to individual bouncing", Mech. Syst. Signal Pr., 76, 394-408. https://doi.org/10.1016/j.ymssp.2016.02.032.
  12. Comer, A.J., Blakeborough, A. and Williams, M.S. (2013), "Rhythmic crowd bobbing on a grandstand simulator", J. Sound Vib., 332(2), 442-454. https://doi.org/10.1016/j.jsv.2012.08.012.
  13. Davenport, A.G. (1961), "The spectrum of horizontal gustiness near the ground in high winds", Quart. J. Roy Meteorol. Soc., 87(372), 194-211. https://doi.org/10.1002/qj.49708737208.
  14. de Brito, V.L. and Pimentel, R.L. (2009), "Cases of collapse of demountable grandstands", J. Perform Constr. Facil., 23(3), 151-159. https://doi.org/10.1061/(asce)cf.1943-5509.0000006.
  15. Duarte, E. and Ji, T. (2009), "Action of individual bouncing on structures", J. Struct. Eng., 135(7), 818-827. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:7(818).
  16. Ellis, B.R. and Ji, T. (2004), "Loads generated by jumping crowds: Numerical modelling", Struct. Eng., 82(17), 35-40.
  17. Ferrarotti, A. and Tubino, F. (2016), "Generalized equivalent spectral model for serviceability analysis of footbridges", J. Bridge Eng., 21(12), 4016091. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000963.
  18. Housner, G.W. (1947). "Characteristics of strong-motion earthquakes", Bull. Seismol. Soc. Am., 37(1), 19-31. https://doi.org/10.1785/BSSA0370010019.
  19. ISO 10137 (2007), Bases for Design of Structures-Serviceability of Buildings and Walkways Against Vibrations, International Organization for Standardization, Geneva, Switzerland.
  20. IStructE (2008), Dynamic Performance Requirements for Permanent Grandstands: Recommendations for Management Design and Assessment, Institution of Structural Engineers, London, UK.
  21. Jones, C.A., Reynolds, P. and Pavic, A. (2011), "Vibration serviceability of stadia structures subjected to dynamic crowd loads: A literature review", J. Sound Vib., 330(8), 1531-1566. https://doi.org/10.1016/j.jsv.2010.10.032.
  22. Lee, S.H., Lee, K.K., Woo, S.S. and Cho, S.H. (2013), "Global vertical mode vibrations due to human group rhythmic movement in a 39 story building structure", Eng. Struct., 57, 296-305. https://doi.org/10.1016/j.engstruct.2013.09.035.
  23. Liu, J., Cao, L. and Chen, Y.F. (2019), "Analytical solution for free vibration of multi-span continuous anisotropic plates by the perturbation method", Struct. Eng. Mech., 69(3), 283-291. https://doi.org/10.12989/sem.2019.69.3.283.
  24. Parkhouse, J.G. and Ewins, D.J. (2006), "Crowd-induced rhythmic loading", Proc. Inst. Civil Eng.-Struct. Build., 159(5), 247-259. https://doi.org/10.1680/stbu.2006.159.5.247.
  25. Piccardo, G. and Tubino, F. (2012), "Equivalent spectral model and maximum dynamic response for the serviceability analysis of footbridges", Eng. Struct., 40, 445-456. https://doi.org/10.1016/j.engstruct.2012.03.005.
  26. Racic, V. and Chen, J. (2015), "Data-driven generator of stochastic dynamic loading due to people bouncing", Comput. Struct., 158, 240-250. https://doi.org/10.1016/j.compstruc.2015.04.013.
  27. Racic, V. and Pavic, A. (2010), "Stochastic approach to modelling of near-periodic jumping loads", Mech. Syst. Signal Pr., 24(8), 3037-3059. https://doi.org/10.1016/j.ymssp.2010.05.019.
  28. Raftoyiannis, I.G. and Michaltsos, G.T. (2018), "Dynamic behavior of footbridges strengthened by external cable systems", Struct. Eng. Mech., 66(5), 595-608. http://doi.org/10.12989/sem.2018.66.5.595.
  29. Sim, J., Blakeborough, A., Williams, M.S. and Parkhouse, G. (2008), "Statistical model of crowd jumping loads", J. Struct. Eng., 134(12), 1852-1861. https://doi.org/10.1061/(asce)0733-9445(2008)134:12(1852).
  30. Van Nimmen, K., Lombaert, G., De Roeck, G. and Van den Broeck, P. (2017), "The impact of vertical human-structure interaction on the response of footbridges to pedestrian excitation", J. Sound Vib., 402, 104-121. https://doi.org/10.1016/j.jsv.2017.05.017.
  31. Vanmarcke, E.H. (1975), "On the distribution of the first-passage time for normal stationary random processes", J. Appl. Mech., 42(1), 215-220. https://doi.org/10.1115/1.3423521.
  32. Venuti, F., Racic, V. and Corbetta, A. (2016), "Modelling framework for dynamic interaction between multiple pedestrians and vertical vibrations of footbridges", J. Sound Vib., 379, 245-263. https://doi.org/10.1016/j.jsv.2016.05.047.
  33. Wang, H., Chen, J. and Nagayama, T. (2019), "Parameter identification of spring-mass-damper model for bouncing people", J. Sound Vib., 456, 13-29. https://doi.org/10.1016/j.jsv.2019.05.034.
  34. Wang, J. and Chen, J. (2017), "A comparative study on different walking load models", Struct. Eng. Mech., 63(6), 847-856. http://doi.org/10.12989/sem.2017.63.6.847.
  35. Wolmuth, B. and Surtees, J. (2003), "Crowd-related failure of bridges", Proc. Inst. Civil Eng.-Civil Eng., 156(3), 116-123. https://doi.org/10.1680/cien.2003.156.3.116.
  36. Xiong, J. and Chen, J. (2018), "Power spectral density function for individual jumping load", Int. J. Struct. Stab. Dyn., 18(02), 1850023. https://doi.org/10.1142/s0219455418500232.
  37. Xiong, J. and Chen, J. (2019a), "A Generative adversarial network model for simulating various types of human-induced loads." Int. J. Struct. Stab. Dyn., 19(08), 1950092. https://doi.org/10.1142/S0219455419500925.
  38. Xiong, J. and Chen, J. (2019b), "Random field model for crowd jumping loads", Struct. Saf., 76, 197-209. https://doi.org/10.1016/j.strusafe.2018.10.001.
  39. Xiong, J., Chen, J. and Caprani, C. (2021), "Spectral analysis of human-structure interaction during crowd jumping", Appl. Math. Model., 89, 610-626. https://doi.org/10.1016/j.apm.2020.07.030.
  40. Zhu, Q., Hui, X., Du, Y. and Zhang, Q. (2019), "A full path assessment approach for vibration serviceability and vibration control of footbridges", Struct. Eng. Mech., 70(6), 765-779. http://doi.org/10.12989/sem.2019.70.6.765.
  41. Zivanovic, S., Pavic, A. and Reynolds, P. (2005), "Vibration serviceability of footbridges under human-induced excitation: A literature review", J. Sound Vib., 279(1-2), 1-74. https://doi.org/10.1016/j.jsv.2004.01.019.
  42. Zivanovic, S., Pavic, A. and Reynolds, P. (2007), "Probability-based prediction of multi-mode vibration response to walking excitation", Eng. Struct., 29(6), 942-954. https://doi.org/10.1016/j.engstruct.2006.07.004.