Technical Papers
Jun 4, 2024

Parameter Optimization of High-Frequency Floor Based on Semirigid Boundary Conditions and Its Effect on the Serviceability of Human-Induced Vibration

Publication: Journal of Structural Engineering
Volume 150, Issue 8

Abstract

The accurate representation of real floor behavior is crucial for assessing human-induced vibration serviceability. Many researchers focus on developing computational models and field testing to reflect actual serviceability conditions. Although traditional boundary conditions are commonly used, limited attention has been given to optimizing these conditions. To begin with, this paper introduced semirigid boundary conditions into a finite-element model of the floor and optimized physical parameters and boundary constraint stiffness using the simulated annealing-particle swarm optimization (SA-PSO) method, resulting in a more realistic computational model. Subsequently, a random crowd load model was established by combining the social force model (SFM) and the pedestrian load model, and a random crowd-floor mutual coupling calculation model was established based on the improved pedestrian biomechanical model. In addition, the mode shape functions of the floor with semirigid boundary conditions were obtained by extracting the optimized mode shape vector of the floor and using cubic spline interpolation. The dynamic response of the floor was computed using the modal analysis method, and the accuracy of the suggested method and model was verified by experiment. Furthermore, the effect on the vibration serviceability of the floor was analyzed under crowd walks randomly on the floor with different boundary conditions both before and after optimization. This study revealed: (1) achieving a computational model consistent with real floors requires optimization of relevant parameters and boundary conditions, reducing the error in floor frequency from 39.48% to 5.44% compared to measured results. (2) The human-induced vibration serviceability for existing floors may be misjudged by using traditional boundary conditions. The mean value of peak acceleration of floor with semirigid boundary conditions increased by 35.92%, with a 42% increase in the probability of serviceability problems compared to the SSCC boundary. (3) High-frequency floors also experience human-induced vibration serviceability issues. For a floor with a fundamental frequency of 10.3540 Hz, simulation and experimental results during five-person random walks indicate that peak acceleration at the middle position of the floor exceeds serviceability limits.

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Data Availability Statement

Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (52168041) and Science and Technology Foundation for Youth of Gansu Province (21JR7RA557). Moreover, the authors are thankful for the literature regarding the model verification.

References

Allen, D. E., and T. M. Murray. 1993. “Design criterion for vibrations due to walking.” Eng. J. 30 (4): 117–129. https://doi.org/10.62913/engj.v30i4.1281.
Bazli, M., M. Heitzmann, and H. Ashrafi. 2022. “Long-span timber flooring systems: A systematic review from structural performance and design considerations to constructability and sustainability aspects.” J. Build. Eng. 48 (May): 103981. https://doi.org/10.1016/j.jobe.2021.103981.
Brownjohn, J. M. W., and C. J. Middleton. 2008. “Procedures for vibration serviceability assessment of high-frequency floors.” Eng. Struct. 30 (6): 1548–1559. https://doi.org/10.1016/j.engstruct.2007.10.006.
Caetano, E., Á. Cunha, F. Magalhães, and C. Moutinho. 2010. “Studies for controlling human-induced vibration of the Pedro e Inês footbridge, Portugal. Part 1: Assessment of dynamic behaviour.” Eng. Struct. 32 (4): 1069–1081. https://doi.org/10.1016/j.engstruct.2009.12.034.
Cao, L., and Y. F. Chen. 2021. “Formulation of human–structure interaction for vibration serviceability of steel–concrete composite floors.” Struct. Control Heal. Monit. 28 (3): e2679. https://doi.org/10.1002/stc.2679.
Chapain, S., and A. M. Aly. 2019. “Vibration attenuation in high-rise buildings to achieve system-level performance under multiple hazards.” Eng. Struct. 197 (Oct): 109352. https://doi.org/10.1016/j.engstruct.2019.109352.
Chen, J., H. Q. Wang, and Y. X. Peng. 2014. “Experimental investigation on Fourier-series model of walking load and its coefficients.” Zhendong yu Chongji/J. Vib. Shock 33 (8): 11–15. https://doi.org/10.13465/j.cnki.jvs.2014.08.003.
da Silva, F. T., H. M. B. F. Brito, and R. L. Pimentel. 2013. “Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges.” Can. J. Civ. Eng. 40 (12): 1196–1204. https://doi.org/10.1139/cjce-2011-0587.
Dong, C. Z., S. Bas, and F. N. Catbas. 2020. “Investigation of vibration serviceability of a footbridge using computer vision-based methods.” Eng. Struct. 224 (Dec): 111224. https://doi.org/10.1016/j.engstruct.2020.111224.
Eftekhari, S. A. 2014. “A note on mathematical treatment of the Dirac-delta function in the differential quadrature bending and forced vibration analysis of beams and rectangular plates subjected to concentrated loads.” Appl. Math. Modell. 39 (20): 6223–6242. https://doi.org/10.1016/j.apm.2015.01.063.
Fujino, Y., B. M. Pacheco, S.-I. Nakamura, and P. Warnitchai. 1993. “Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge.” Earthquake Eng. Struct. Dyn. 22 (9): 741–758. https://doi.org/10.1002/eqe.4290220902.
Gonçalves, M. S., A. Pavic, and R. L. Pimentel. 2020. “Vibration serviceability assessment of office floors for realistic walking and floor layout scenarios: Literature review.” Adv. Struct. Eng. 23 (6): 1238–1255. https://doi.org/10.1177/1369433219888753.
Gong, M., Y. Li, R. Shen, and X. Wei. 2021. “Glass suspension footbridge: Human-induced vibration, serviceability evaluation, and vibration mitigation.” J. Bridg. Eng. 26 (11): 05021014. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001788.
Gorman, D. J. 2003. “Free vibration analysis of corner-supported rectangular plates with symmetrically distributed edge beams.” J. Sound Vib. 263 (5): 979–1003. https://doi.org/10.1016/S0022-460X(03)00269-4.
Helbing, D., I. Farkas, and T. Vicsek. 2000. “Simulating dynamical features of escape panic.” Nature 407 (6803): 487–490. https://doi.org/10.1038/35035023.
Helbing, D., I. Farkas, and T. Vicsek. 2003. “Simulation software for ‘simulating dynamical features of escape panic.’” Accessed March 24, 2003. https://xxx.lanl.gov, paper cond-mat/0302021.
Huang, H., Y. Gao, and W. S. Chang. 2020. “Human-induced vibration of cross-laminated timber (CLT) floor under different boundary conditions.” Eng. Struct. 204 (Feb): 110016. https://doi.org/10.1016/j.engstruct.2019.110016.
ISO. 2007. Bases for design of structures serviceability of buildings and walkways against vibrations. ISO 10137. Geneva: ISO.
Jiang, Y., B. Chen, X. Li, and Z. Ding. 2020. “Dynamic navigation field in the social force model for pedestrian evacuation.” Appl. Math. Modell. 80 (Apr): 815–826. https://doi.org/10.1016/j.apm.2019.10.016.
Kerr, S. C., and N. W. M. Bishop. 2001. “Human induced loading on flexible staircases.” Eng. Struct. 23 (1): 37–45. https://doi.org/10.1016/S0141-0296(00)00020-1.
Kumarappan, N., and K. Suresh. 2015. “Combined SA PSO method for transmission constrained maintenance scheduling using levelized risk method.” Int. J. Electr. Power Energy Syst. 73 (Dec): 1025–1034. https://doi.org/10.1016/j.ijepes.2015.06.026.
Li, Y., M. Chen, Z. Dou, X. Zheng, Y. Cheng, and A. Mebarki. 2019. “A review of cellular automata models for crowd evacuation.” Phys. A Stat. Mech. Appl. 526 (Apr): 120752. https://doi.org/10.1016/j.physa.2019.03.117.
Liu, D., and B. Davis. 2015. “Walking vibration response of high-frequency floors supporting sensitive equipment.” J. Struct. Eng. 141 (8): 04014199. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001175.
Liu, K., L. Liu, Q. Zhu, Y. Liu, and F. Zhou. 2021. “Dynamic testing and numerical simulation of human-induced vibration of cantilevered floor with tuned mass dampers.” Structures 34 (Dec): 1475–1488. https://doi.org/10.1016/j.istruc.2021.08.079.
Lv, Q., Y. Lu, and Y. Liu. 2021. “Vibration serviceability of suspended floor: Full-scale experimental study and assessment.” Structures 34 (Dec): 1651–1664. https://doi.org/10.1016/j.istruc.2021.08.120.
Ma, R., L. Ke, D. Wang, A. Chen, and Z. Pan. 2018. “Experimental study on pedestrians’ perception of human-induced vibrations of footbridges.” Int. J. Struct. Stab. Dyn. 18 (10): 1850116. https://doi.org/10.1142/S021945541850116X.
Middleton, C. J., and J. M. W. Brownjohn. 2010. “Response of high frequency floors: A literature review.” Eng. Struct. 32 (2): 337–352. https://doi.org/10.1016/j.engstruct.2009.11.003.
Mohammed, A. S., A. Pavic, and V. Racic. 2018. “Improved model for human induced vibrations of high-frequency floors.” Eng. Struct. 168 (May): 950–966. https://doi.org/10.1016/j.engstruct.2018.04.093.
Muhammad, Z., P. Reynolds, O. Avci, and M. Hussein. 2018. “Review of pedestrian load models for vibration serviceability assessment of floor structures.” Vibration 2 (1): 1–24. https://doi.org/10.3390/vibration2010001.
Pu, X., T. He, and Q. Zhu. 2023. “Considering the effect of obstacles and semi-rigid boundary conditions on the dynamic response of the floor under random crowd-structure interaction.” Acta Mech. 234 (9): 3821–3841. https://doi.org/10.1007/s00707-023-03595-2.
Schubert Pfeil, M., W. Diniz Varela, and N. de Paula Amador da Costa. 2022. “Experimental calibration of a one degree of freedom biodynamic model to simulate human walking-structure interaction.” Eng. Struct. 262 (Jul): 114330. https://doi.org/10.1016/j.engstruct.2022.114330.
Takabatake, H., and Y. Nagareda. 1999. “A simplified analysis of elastic plates with edge beams.” Comput. Struct. 70 (2): 129–139. https://doi.org/10.1016/S0045-7949(98)00164-3.
Venuti, F., and L. Bruno. 2007. “An interpretative model of the pedestrian fundamental relation.” C. R. Mec 335 (4): 194–200. https://doi.org/10.1016/j.crme.2007.03.008.
Venuti, F., and F. Tubino. 2021. “Human-induced loading and dynamic response of footbridges in the vertical direction due to restricted pedestrian traffic.” Struct. Infrastruct. Eng. 17 (10): 1431–1445. https://doi.org/10.1080/15732479.2021.1897630.
Wang, H., Q. Ge, D. Zeng, Z. Zhang, and J. Chen. 2023a. “Human-induced vibration serviceability: From dynamic load measurement towards the performance-based structural design.” Buildings 13 (8): 1977. https://doi.org/10.3390/buildings13081977.
Wang, J., and J. Chen. 2022. “Equivalent dynamic load factor for crowd walking loads.” J. Struct. Eng. 148 (10): 1–15. https://doi.org/10.1061/(asce)st.1943-541x.0003463.
Wang, Z., L. Song, Z. Cheng, H. Yang, J. Wen, and M. Qi. 2023b. “Finite element model for vibration serviceability evaluation of a suspended floor with and without tuned mass dampers.” Buildings 13 (2): 309. https://doi.org/10.3390/buildings13020309.
Willford, M. R., and P. Young. 2006. A design guide for footfall induced vibration of structures. London: Concrete Society for the Concrete Centre.
Wu, Z., Z. Wu, and J. Zhang. 2017. “An improved FCM algorithm with adaptive weights based on SA-PSO.” Neural Comput. Appl. 28 (10): 3113–3118. https://doi.org/10.1007/s00521-016-2786-6.
Xu, H., J. Du, and W. L. Li. 2010. “Vibrations of rectangular plates reinforced by any number of beams of arbitrary lengths and placement angles.” J. Sound Vib. 329 (18): 3759–3779. https://doi.org/10.1016/j.jsv.2010.03.023.
Yang, X., X. Yang, Y. Li, J. Zhang, and Y. Kang. 2021. “Obstacle avoidance in the improved social force model based on ant colony optimization during pedestrian evacuation.” Physica A 583 (Feb): 126256. https://doi.org/10.1016/j.physa.2021.126256.
Zhang, S., and L. Xu. 2020. “Human-induced vibration of cold-formed steel floor systems: Parametric studies.” Adv. Struct. Eng. 23 (10): 2030–2043. https://doi.org/10.1177/1369433220904013.
Zhang, S., and L. Xu. 2022. “Vibration serviceability evaluation of lightweight cold-formed steel floor systems.” Structures 38 (Jun): 1368–1379. https://doi.org/10.1016/j.istruc.2022.02.009.
Zhao, R., Y. Zhai, L. Qu, R. Wang, Y. Huang, and Q. Dong. 2021. “A continuous floor field cellular automata model with interaction area for crowd evacuation.” Physica A 575 (Aug): 126049. https://doi.org/10.1016/j.physa.2021.126049.
Zhou, J., Y. Guo, S. Dong, M. Zhang, and T. Mao. 2019. “Simulation of pedestrian evacuation route choice using social force model in large-scale public space: Comparison of five evacuation strategies.” PLoS One 14 (9): e0221872. https://doi.org/10.1371/journal.pone.0221872.
Zhu, Q., K. Liu, L. Liu, Y. Du, and S. Zivanovic. 2020. “Experimental and numerical analysis on serviceability of cantilevered floor based on human-structure interaction.” J. Constr. Steel Res. 173 (Oct): 106184. https://doi.org/10.1016/j.jcsr.2020.106184.
Živanović, S. 2012. “Benchmark footbridge for vibration serviceability assessment under the vertical component of pedestrian load.” J. Struct. Eng. 138 (10): 1193–1202. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000571.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 150Issue 8August 2024

History

Received: Oct 19, 2023
Accepted: Feb 26, 2024
Published online: Jun 4, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 4, 2024

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Xinglong Pu [email protected]
Ph.D. Candidate, Institute of Earthquake Protection and Disaster Mitigation, Lanzhou Univ. of Technology, Lanzhou 730050, China. Email: [email protected]
Professor, School of Sciences, Lanzhou Univ. of Technology, Lanzhou 730050, China. Email: [email protected]
Qiankun Zhu [email protected]
Professor, Institute of Earthquake Protection and Disaster Mitigation, Lanzhou Univ. of Technology, Lanzhou 730050, China (corresponding author). Email: [email protected]

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