In the research of autonomous trucks and bridge interaction vibration, fatigue damage of bridge is of high concern. This article investigates the influence of truck platoon spacing on the vibration of the bridge. The relationship among the platoon spacing, the dynamic load and vibration frequency of bridges is analyzed through the oscillators and bridge interaction model by time frozen technique, because of the time-varying effect of the theoretical model. To further analyze the bridge loading caused by the different vehicle platoons on the bridge, an energy-related evaluation index, Action, was established. At the same time, the theoretical model is simplified into the multiple moving loads and bridge vibration model, so as to eliminate the time-varying effect and gain physical insights. The theoretical formula of optimal platoon spacing with two vehicles is derived. Finally, the parameters (the number of vehicles, dynamic load and frequency, etc.) are dimensionless simplified, and their influence on Action is analyzed. This paper focuses on the impact of vehicle platoon spacing on bridge vibration and provides relevant guidance in this area.
AlahmadiMDAlzahraniAS (2025) Improving freight traffic efficiency at urban intersections using heavy vehicle platooning. Applied Sciences15: 2682. https://doi.org/10.3390/app15052682
2.
AloisioAContentoAAlaggioR, et al. (2023) Physics-based models, surrogate models and experimental assessment of the vehicle–bridge interaction in braking conditions. Mechanical Systems and Signal Processing194: 110276.
3.
Angelo AloisioMAAlaggioR (2024) Probabilistic comparative analysis of vehicle–bridge interaction models for predicting bridge response under moving vehicles. Journal of Engineering Mechanics150: 14. https://doi.org/10.1061/jenmdt.emeng-7437
4.
BradySPO’BrienEJ (2006) Effect of vehicle velocity on the dynamic amplification of two vehicles crossing a simply supported bridge. Journal of Bridge Engineering11: 250–256. https://doi.org/10.1061/(asce)1084-0702(2006)11:2(250)
5.
ChangT-P (2014) Stochastic dynamic finite element analysis of bridge–vehicle system subjected to random material properties and loadings. Applied Mathematics and Computation242: 20–35. https://doi.org/10.1016/j.amc.2014.05.038
6.
Couto BraguimTLouPNassifH (2021) Truck platooning to minimize load-induced fatigue in steel girder bridges. Transportation Research Record2675: 146–154. https://doi.org/10.1177/0361198120973657
7.
ElshazliMTHusseinDBhatG, et al. (2024) Advancing infrastructure resilience: machine learning-based prediction of bridges’ rating factors under autonomous truck platoons. Journal of Infrastructure Preservation and Resilience5: 5. https://doi.org/10.1186/s43065-024-00096-x
8.
GaoHYangB (2020) Parametric vibration of a flexible structure excited by periodic passage of moving oscillators. Journal of Applied Mechanics87: 071001. https://doi.org/10.1115/1.4046781
9.
GeCTanCALinK, et al. (2021) On the efficacy and accuracy of freezing technique for the response analysis of time-varying vehicle-bridge interaction systems. Journal of Sound and Vibration514: 116453. https://doi.org/10.1016/j.jsv.2021.116453
HeHYangC (2025) Automated truck platooning–bridge interaction: assessing dynamic impacts on drilled shaft foundations. Journal of Bridge Engineering30: 04025015. https://doi.org/10.1061/jbenf2.beeng-7052
12.
KunzeRHaberstrohMRamakersR, et al. (2011a) Automated truck platoons on motorways–a contribution to the safety on roads. In: Automation, Communication and Cybernetics in Science and Engineering 2009/2010. Springer, pp. 415–426.
13.
KunzeRRamakersRHenningK, et al. (2011b) Organization and operation of electronically coupled truck platoons on German motorways. In” Automation, Communication and Cybernetics in Science and Engineering 2009/2010. Springer, pp. 427–439.
14.
LawSSZhuXQ (2005) Bridge dynamic responses due to road surface roughness and braking of vehicle. Journal of Sound and Vibration282: 805–830. https://doi.org/10.1016/j.jsv.2004.03.032
15.
LiKIoannouP (2004) Modeling of traffic flow of automated vehicles. IEEE Transactions on Intelligent Transportation Systems5: 99–113. https://doi.org/10.1109/tits.2004.828170
16.
LinKTanCAGeC, et al. (2022) Time-varying transmissibility analysis of vehicle-bridge interaction systems with application to bridge-friendly vehicles. International Journal of Structural Stability and Dynamics22(05): 2250022. https://doi.org/10.1142/s0219455422500225
O’BrienECareyCKeenahanJ (2015) Bridge damage detection using ambient traffic and moving force identification. Structural Control and Health Monitoring22: 1396–1407. https://doi.org/10.1002/stc.1749
RebeloMRafaelSBandeiraJM (2024) Vehicle platooning: a detailed literature review on environmental impacts and future research directions. Future Transportation4: 591–607. https://doi.org/10.3390/futuretransp4020028
ScottMSchumacherTUnnikrishnanA, et al. (2024) Impact of Truck Platooning on Loading of Bridges in Oregon. Oregon Department of Transportation. Research Section.
YanLLiJHeX, et al. (2025) Ride comfort assessment of road vehicles on a long-span truss girder suspension bridge under crosswinds. Engineering Structures322: 119112. https://doi.org/10.1016/j.engstruct.2024.119112
26.
YangYLiYChangKC (2014) Constructing the mode shapes of a bridge from a passing vehicle: a theoretical study. Smart Structures and Systems13: 797–819. https://doi.org/10.12989/sss.2014.13.5.797
27.
YangYLiuYXuH (2023) Recovering mode shapes of curved bridges by a scanning vehicle. International Journal of Mechanical Sciences253: 108404. https://doi.org/10.1016/j.ijmecsci.2023.108404
28.
YangBSteelmanJSPuckettJA, et al. (2024) Reliability-based service III evaluation for prestressed girder bridges under platoon loads. Transportation Research Record2678: 515–536. https://doi.org/10.1177/03611981231208200
