Suspended monorail system dynamics: fundamental and practice

Abstract

Urban transportation systems are facing severe challenges due to the rapid growth of the urban population, especially in China. Suspended monorail system (SMS), as a sky rail transportation form, can effectively alleviate urban traffic congestion due to its independent right-of-way and minimal ground footprint. However, the SMS possesses a special traveling system with unique vehicle structure and bridge configuration, which results in significant differences in both the mechanisms and dynamics problems associated with train–bridge interaction (TBI) when contrasted with those of traditional railway systems. Therefore, a thorough understanding of the SMS dynamics is essential for ensuring the operational safety of the system. This article presents a state-of-the-art review of the TBI modeling methodologies, critical dynamic features, field tests, and practice of the SMS in China. Firstly, the development history, technical features, and potential dynamics problems of the SMS are briefly described, followed by the mechanical characteristics and mechanisms of the train–bridge interactive systems. Then, the modeling methodology of the fundamental elements in the suspended monorail TBI is systematically reviewed, including the suspended train subsystem, bridge subsystem, train–bridge interaction relationships, system excitations, and solution method. Further, the typical dynamic features of the TBI under various operational scenarios are elaborated, including different train speeds, a variety of line sections, and a natural wind environment. Finally, the first new energy-based SMS test line in the world is systematically introduced, including the composition and functionality of the system, the details of the conducted field tests, and the measured results of the typical dynamic responses. At the end of the paper, both the guidance on further improvement of the SMS and future research topics are proposed.

Keywords

Suspended monorail system / Train–bridge dynamic interaction / Modeling methodology / Experimental investigation / Dynamic features / Crosswind

References

[1] GravaSUrban transportation systems. Choices for communities, 2003, New York. McGraw-Hill.

[2] SimpsonBUrban public transport today, 1993, London. Routledge.

[3] CaiC, HeQ, ZhuS, et al.. Dynamic interaction of suspension-type monorail vehicle and bridge: numerical simulation and experiment. Mech Syst Signal Pr, 2019, 118: 388-407.

[4] KikuchiS, OnakaA. Monorail development and application in Japan. J Adv Transport, 1988, 22(1): 17-38.

[5] WeiL, ZengJ, HuangC, et al.. Experimental and numerical investigations on longitudinal vibration of suspended monorail trains induced by bogie pitching motion. Proc Inst Mech Eng F-J Rail Rapid Transit, 2021, 236(4): 418-433.

[6] Bakhit Mabrouk WA (2015) Development of mathematical model for monorail suspension system under different track conditions. In: Dissertation, Universiti Tun Hussein Onn Malaysia

[7] LiF, XuW, AnQ. Development and current status of suspended monorail vehicle. Elec Drive Locomoti, 2014, 76(2): 16-20

[8] Kennedy R (2004) Considering monorail rapid transit for North American cities. In: Narrative report.

[9] Bao Y (2019) Coupling vibration of vehicle bridge system under wind environment for suspended monorail transit. Dissertation, Southwest Jiaotong University (in Chinese)

[10] He Q (2020) Theoretical analysis and experimental study on vehicle–bridge coupling vibration of suspended monorail traffic. Dissertation, Southwest Jiaotong University (in Chinese)

[11] HeQ, YangY, CaiC, et al.. Experimental investigation on coupled vibration features of suspended monorail train–bridge system under constant speed and braking conditions. Int J Struct Stab Dyn, 2021, 21122150177.

[12] HeQ, CaiC, ZhaiW, et al.. Field measurement of the dynamic responses of a suspended monorail train–bridge system. Proc Inst Mech Eng F-J Rail Rapid Transit, 2020, 234(10): 1093-1108.

[13] NaeimiM, TatariM, EsmaeilzadehA, et al.. Dynamic interaction of the monorail-bridge system using a combined finite element multibody-based model. Proc Inst Mech Eng K-J Multidyn, 2015, 229(2): 132-151

[14] ShamsiM, GhanbariA. Nonlinear dynamic analysis of Qom monorail bridge considering soil pile-bridge-train interaction. Transp Geotech, 2020, 22. 100309

[15] ShiJ, WeiQ, ZhaoY. Analysis of dynamic response of the high-speed EMS maglev vehicle/guideway coupling system with random irregularity. Veh Syst Dyn, 2007, 45(12): 1077-1095.

[16] LiM, GaoD, LiT, et al.. Experimental investigation on vibration characteristics of the medium–low-speed maglev vehicle–turnout coupled system. Railw Eng Sci, 2022, 30: 242-261.

[17] ZhaiW, HanZ, ChenZ, et al.. Train-track-bridge dynamic interaction: a state-of-the-art review. Veh Syst Dyn, 2019, 57(7): 984-1027.

[18] YangYB, YauJD, WuYSVehicle–bridge interaction dynamics: with applications to high-speed railways, 2004, Singapore. World Scientific Publishing Company. .

[19] XiaH, ZhangN, GuoWDynamic interaction of train–bridge systems in high-speed railways: theory and applications, 2018, Berlin. Springer. .

[20] ArvidssonT, KaroumiR. Train–bridge interaction - a review and discussion of key model parameters. Int J Rail Transp, 2014, 2: 147-186.

[21] ZhaiW, XiaH, CaiC, et al.. High-speed train-track-bridge dynamic interactions - part I: theoretical model and numerical simulation. Int J Rail Transp, 2013, 1(1–2): 3-24.

[22] ZhangN, XiaH. Dynamic analysis of coupled vehicle–bridge system based on inter-system iteration method. Comput Struct, 2013, 114: 26-34.

[23] ZhuZ, GongW, WangL. An efficient multi-time-step method for train-track-bridge interaction. Comput Struct, 2018, 196: 36-48.

[24] AntolínP, ZhangN, GoicoleaJM, et al.. Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways. J Sound Vib, 2013, 332: 1231-1251.

[25] LiangL, DhanasekarM, ThambiratnamDP. Dynamic response of the train-track-bridge system subjected to derailment impacts. Veh Syst Dyn, 2018, 56(4): 638-657.

[26] ZhaiW, XiaH, CaiC, et al.. High-speed train-track-bridge dynamic interactions - part II: experimental validation and engineering application. Int J Rail Transp, 2013, 1(1–2): 25-41.

[27] LiY, XiangH, WangZ, et al.. A comprehensive review on coupling vibrations of train–bridge systems under external excitations. Railw Eng Sci, 2022, 30: 383-401.

[28] ArvidssonT, AnderssonA, KaroumiR. Train running safety on non-ballasted bridges. Int J Rail Transp, 2019, 7(1): 1-22.

[29] ZhangN, ZhouZ, WuZ. Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method. Railw Eng Sci, 2022, 30: 41-56.

[30] TanabeM, SogabeM, WakuiH, et al.. Exact time integration for dynamic interaction of high-speed train and railway structure including derailment during an earthquake. J Comput Nonlinear Dyn, 2016, 113. 031004

[31] Li X, He H, Wang M et al (2023) Influence of long-span bridge deformation on driving quality of high-speed trains. In: Int J Rail Transp 12(4):690–708

[32] MolinerE, Martínez-RodrigoMD, MuserosP. Dynamic performance of existing double track railway bridges at resonance with the increase of the operational line speed. Eng Struct, 2017, 132: 98-109.

[33] SilvaR, RibeiroD, CostaC, et al.. Experimental validation of a non-linear train-track-bridge dynamic model of a stone arch railway bridge under freight traffic. Int J Rail Transp, 2022, 12(1): 102-133.

[34] YangY, LinC. Vehicle–bridge interaction dynamics and potential applications. J Sound Vib, 2005, 284(1–2): 205-226.

[35] MontenegroPA, CalçadaR, CarvalhoH, et al.. Stability of a train running over the Volga river high-speed railway bridge during crosswinds. Struct Infrastruct Eng, 2020, 16(8): 1121-1137.

[36] GaoZY, TianB, WuDP, et al.. Study on semi-active control of running stability in the high-speed train under unsteady aerodynamic loads and track excitation. Veh Syst Dyn, 2021, 59(1): 101-114.

[37] SunZ, ZhangY, GuoD, et al.. Research on running stability of CRH3 high speed trains passing by each other. Eng Appl Comput Fluid Mech, 2014, 8(1): 140-157

[38] WangQ, WangZ, MoJ, et al.. Modelling and stability analysis of a high-speed train braking system. Int J Mech Sci, 2023, 250. 108315

[39] ShebaniA, IwnickiS. Prediction of wheel and rail wear under different contact conditions using artificial neural networks. Wear, 2018, 406: 173-184.

[40] EnblomR. Deterioration mechanisms in the wheel–rail interface with focus on wear prediction: a literature review. Veh Syst Dyn, 2009, 47(6): 661-700.

[41] ChoiJ, KimB. Failure analysis of anchor bolt of rail fastening system for direct fixation track. Eng Fail Anal, 2020, 112. 104513

[42] ZhuS, CaiC. Interface damage and its effect on vibrations of slab track under temperature and vehicle dynamic loads. Int J Non-Linear Mech, 2014, 58: 222-232.

[43] CaoS, YangR, SuC, et al.. Damage mechanism of slab track under the coupling effects of train load and water. Eng Fract Mech, 2016, 163: 160-175.

[44] MontenegroPA, CarvalhoH, RibeiroD, et al.. Assessment of train running safety on bridges: a literature review. Eng Struct, 2021, 241. 112425

[45] OlmosJM, AstizMÁ. Non-linear vehicle–bridge-wind interaction model for running safety assessment of high-speed trains over a high-pier viaduct. J Sound Vib, 2018, 419: 63-89.

[46] GranatoEC, FerreiraG, MontenegroP, et al.. Probabilistic analysis of train running safety on bridges: a state-of-the-art review. Int J Rail Transp, 2025.

[47] LengH, RenL, JiY, et al.. Radial adjustment mechanism of a newly designed coupled bogie for the straddle-type monorail vehicle. Veh Syst Dyn, 2020, 58(9): 1407-1427.

[48] ZhouJ, DuZ, YangZ, et al.. Dynamic parameters optimization of straddle-type monorail vehicles based multiobjective collaborative optimization algorithm. Veh Syst Dyn, 2020, 58(3): 357-376.

[49] ShamsiM, ZakerinejadM, VakiliAH. Seismic analysis of soil-pile-bridge-train interaction for isolated monorail and railway bridges under coupled lateral-vertical ground motions. Eng Struct, 2021, 248. 113258

[50] ZhouJ, JiangW, HuangS, et al.. Shimmy vibration control of straddle-type monorail vehicle with time delay compensation based on signal influence of multisource random track surface excitation. Mech Syst Signal Process, 2025, 230. 112620

[51] WenX, NieY, DuZ, et al.. Operational safety assessment of straddle-type monorail vehicle system based on cloud model and improved CRITIC method. Eng Fail Anal, 2022, 139. 106463

[52] WangG, LiK, ZhouH. Abnormal wear analysis of straddle-type monorail vehicle running wheel tire. Adv Mech Eng, 2019, 11(11): 1-16.

[53] LeeCH, KimCW, KawataniM, et al.. Dynamic response analysis of monorail bridges under moving trains and riding comfort of trains. Eng Struct, 2005, 27(14): 1999-2013.

[54] LeeCH, KawataniM, KimCW, et al.. Dynamic response of a monorail steel bridge under a moving train. J Sound Vib, 2006, 294(3): 562-579.

[55] HeQ, YangY, CaiC, et al.. An efficient modeling methodology of monorail train and large-scale bridge interaction based on moving element technology. Comput Struct, 2024, 300. 107417

[56] HeQ, CaiC, ZhuS, et al.. An improved dynamic model of suspended monorail train–bridge system considering a tyre model with patch contact. Mech Syst Signal Pr, 2020, 14410. 106865

[57] YangY, HeQ, CaiC, et al.. Coupled vibration analysis of suspended monorail train and curved bridge considering nonlinear wheel–track contact relation. Vehicle Syst Dyn, 2022, 60(8): 2658-2685.

[58] BaoY, ZhaiW, CaiC, et al.. Dynamic interaction analysis of suspended monorail vehicle and bridge subject to crosswinds. Mech Syst Signal Process, 2021, 156. 107707

[59] BaoY, ZhaiW, CaiC, et al.. Effect of the combined centre of gravity height on the ride comfort of suspended monorail train under crosswinds. Veh Syst Dyn, 2022, 61(8): 1954-1972.

[60] ZhaiW, WangK, CaiC. Fundamentals of vehicle–track coupled dynamics. Vehicle Syst Dyn, 2009, 47(11): 1349-1376.

[61] ZhaiWVehicle–track coupled dynamics: theory and applications, 2020, Singapore. Springer. .

[62] Meisinger R (2009) Dynamic analysis of the Dortmund University campus sky train, Nürnberg, Germany, Technische Hochschule Nürnberg Georg Simon Ohm

[63] LvK, WangK, ChenZ, et al.. (2017) Influence of wheel eccentricity on vertical vibration of suspended monorail vehicle: experiment and simulation. Shock Vib, 2017, 1: 1-10

[64] JiangY, WuP, ZengJ, et al.. Researches on the resonance of a new type of suspended monorail vehicle–bridge coupling system based on modal analysis and rigid-flexible coupling dynamics. Veh Syst Dyn, 2019, 59(1): 135-154.

[65] HeQ, YangY, CaiC, et al.. Influences of guideway geometry parameters and track irregularity on dynamic performances of suspended monorail vehicle-guideway system. Struct Eng Mech, 2022, 82(1): 1-16

[66] HeQ, CaiC, ZhaiW, et al.. Improvement on curve negotiation performance of suspended monorail vehicle considering flexible guideway. Int J Str Stab Dyn, 2020, 2052050057.

[67] HeQ, LiS, XuX, et al.. An effective secondary suspension system for isolating the high-frequency vibrations of suspended monorail vehicle running on a flexible track beam. Veh Syst Dyn, 2025, 63(3): 475-493.

[68] WangL, HeQ, YangY, et al.. Research on influences of beam joint impact on dynamic features of suspended monorail vehicle–bridge system. Railw Standard Design, 2023, 68(10): 1-13(in Chinese)

[69] CaiC, ChenS. Framework of vehicle–bridge-wind dynamic analysis. J Wind Eng Ind Aerodyn, 2004, 92(7–8): 579-607.

[70] LiY, LiaoH, QiangS. Simplifying the simulation of stochastic wind velocity fields for long cable-stayed bridges. Comput Struct, 2004, 82(20–21): 1591-1598.

[71] ZhangZ, LinJ, ZhangY, et al.. Non-stationary random vibration analysis for train–bridge systems subjected to horizontal earthquakes. Eng Struct, 2010, 32: 3571-3582.

[72] ZhaiW. Two simple fast integration methods for large-scale dynamic problems in engineering. Int J Numer Methods Eng, 1996, 39: 4199-4214.

[73] QuS, YangJ, ZhuS, et al.. Experimental study on ground vibration induced by double-line subway trains and road traffic. Transp Geotech, 2021, 29. 100564

[74] KimYS, LimTK, ParkSH, et al.. Dynamic model for ride comfort evaluations of the rubber tired light rail vehicle. Veh Syst Dyn, 2008, 46(11): 1061-1082.

[75] ShanY, WangB, ZhouS, et al.. Dynamic analysis of tram vehicles coupled with the track system based on staggered iterative algorithm. J Comput Nonlinear Dyn, 2020, 156. 061002

[76] ChenZ, ZhaiW, LvK, et al.. Investigation on influences of the suspension parameters on running stability for suspended monorail vehicle. J Railw Sci Eng, 2018, 15(10): 2647-2653

[77] KouJ, YuH, LiZ, et al.. Analyses on line dynamic response of unload and load vehicles of suspended monorail. Railw Standard Design, 2019, 63(7): 62-65

[78] ChenZ, ZhaiW, ZhuS, et al.. Performance study on the secondary suspension system of a suspended monorail vehicle based on the quasi-zero-stiffness theory. J Vib Shock, 2019, 38(2): 13-17(in Chinese)

[79] BaoY, LiY, DingJ. A case study of dynamic response analysis and safety assessment for a suspended monorail system. Int J Environ Res Public Health, 2016, 13. 1121

[80] HeQ, CaiC, ZhuS, et al.. Key parameter selection of suspended monorail system based on vehicle–bridge dynamical interaction analysis. Veh Syst Dyn, 2019, 58(3): 339-356.

[81] GuoS, HangC, HuJ, et al.. Research on plane curve parameter of suspended monorail based on comfort. Railw Standard Design, 2019, 63(7): 46-51

[82] KouJ, YuH, XieY, et al.. Influence of transition curve types on dynamic response of suspended monorail vehicle. J Beijing Jiaotong Univ, 2020, 4: 102-107

[83] WangJ. Research on the transition curve length of suspended monorail base on lean-time-variable rate. Railw Standard Design, 2018, 62(12): 35-39

[84] Hu Y, Xiao J, Lin H et al (2016) Research on appropriate track gauge at curved section of suspended monorail transit system. Railw Eng 514(12):86–89 (in Chinese)

[85] YangZ, CaiC, LingL, et al.. Dynamic performance of suspended monorail train passing through curve section. Railw Eng, 2021, 60(10): 146-150

[86] YuH, XieY, KouJ, et al.. Study on the standard value of passenger comfort control for suspended monorail planar circular curve. Railw Standard Design, 2019, 63(7): 57-61

[87] YangY, HeQ, CaiC, et al.. A novel 3D train–bridge interaction model for monorail system considering nonlinear wheel–track slipping behavior. Nonlinear Dynam, 2024, 112: 3265-3301.

[88] YangP, BaoY, ZengY, et al.. Type selection design for bridge structure of suspended monorail transit system. J Railw Eng Soc, 2016, 214(7): 30-35

[89] QiuJ, ZhengK, XiongZ. Static analysis and section optimization of continuous track girder bridge in suspension monorail traffic system. Railw Standard Design, 2020, 64(11): 73-78

[90] WeiJ, ChenT, HuangD, et al.. Pier-beam integral analysis of suspended monorail traffic system. Railw Standard Design, 2019, 49(1): 36-41

[91] BaoY, XiangH, LiY, et al.. Study of wind–vehicle–bridge system of suspended monorail during the meeting of two trains. Adv Struct Eng, 2019, 22(8): 1988-1997.

[92] ZouY, LiuZ, ShiK, et al.. Experimental study of aerodynamic interference effects for a suspended monorail vehicle–bridge system using a wireless acquisition system. Sensors, 2021, 215841.

[93] ZouY, LiuZ, ShiK, et al.. Experimental study of the aerodynamic characteristics of a suspended monorail vehicle–bridge system under crosswinds. Int J Struct Stab Dyn, 2022, 2210. 2241007

[94] BaoY, ZhaiW, CaiC, et al.. Experimental study on the influence of rolling angle on aerodynamic characteristics of suspended monorail trains. J Wind Eng Ind Aerodyn, 2023, 232. 105289

[95] JTG/T 3360–01–2018. Wind-resistant design specification for highway bridges. China Communications Press Co. Ltd, Beijing, 2018 (in Chinese)

[96] ZouY, LiuZ, ShiK, et al.. Analysis of effects of aerodynamic interference on dynamic response of suspended monorail wind–vehicle–bridge system using joint simulation approach. Struct, 2022, 45: 179-198.

[97] ChenX, WangB, ZhuL, et al.. Numerical study on surface distributed vortex-induced force on a flat-steel-box girder. Eng Appl Comput Fluid, 2018, 12(1): 41-56

[98] HeX, KangX, YanL, et al.. Numerical investigation of flow structures and aerodynamic interference around stationary parallel box girders. J Wind Eng Ind Aerod, 2021, 215. 104610

[99] BaoY, ZhaiW, CaiC, et al.. Experimental and numerical study on aerodynamic characteristics of suspended monorail trains passing each other under crosswinds. Wind Struct, 2023, 37(5): 361-373

[100] LiY, YuC, ChenX, et al.. An efficient Cholesky decomposition and applications for the simulation of large-scale random wind velocity fields. Adv Struct Eng, 2018, 22(6): 1255-1265.

[101] PengL, HuangG, KareemA, et al.. An efficient space-time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations. Probabilist Eng Mech, 2016, 43: 156-168.

[102] MontenegroPA, BarbosaD, CarvalhoH, et al.. Dynamic effects on a train–bridge system caused by stochastically generated turbulent wind fields. J Wind Eng Ind Aerodyn, 2020, 211110430

[103] CooperRK. Atmospheric turbulence with respect to moving ground vehicles. J Wind Eng Ind Aerod, 1984, 17(2): 215-238.

[104] LiY, QiangS, LiaoH, et al.. Dynamics of wind–rail–vehicle–bridge systems. J Wind Eng Ind Aerodyn, 2005, 93(6): 483-507.

[105] TiZ, ZhouY, LiY. On-site wave-wind observation and spectral investigation of dynamic behaviors for sea-crossing bridge during tropical cyclone. Eng Struct, 2023, 283. 115907

[106] LiX, TanY, QiuX, et al.. Wind tunnel measurement of aerodynamic characteristics of trains passing each other on a simply supported box girder bridge. Railw Eng Sci, 2021, 29(2): 152-162.

[107] XiangH, LiY, ChenSR, et al.. A wind tunnel test method on aerodynamic characteristics of moving vehicles under crosswinds. J Wind Eng Ind Aerodyn, 2017, 163: 15-23.

[108] ZhuL, LiL, XuY, et al.. Wind tunnel investigations of aerodynamic coefficients of road vehicles on bridge deck. J Fluid Struct, 2012, 30: 35-50.

[109] HeX, ZouY, WangH, et al.. Aerodynamic characteristics of a trailing rail vehicles on viaduct based on still wind tunnel experiments. J Wind Eng Ind Aerod, 2014, 135: 22-33.

[110] BakerC, CheliF, OrellanoA, et al.. Cross-wind effects on road and rail vehicles. Veh Syst Dyn, 2009, 47(8): 983-1022.

[111] BakerCJ. The simulation of unsteady aerodynamic cross wind forces on vehicles. J Wind Eng Ind Aerod, 2010, 98(2): 88-99.

[112] XuX, LiY, ZhuS. Non-uniform wind excitation on dynamic responses of vehicle running on bridge. J Wind Eng Ind Aerod, 2023, 233. 105301

[113] YanL, ZhuL, HeX, et al.. Experimental determination of aerodynamic admittance functions of a bridge deck considering oscillation effect. J Wind Eng Ind Aerod, 2019, 190: 83-97.

[114] YangW, YueH, DengE, et al.. Comparison of aerodynamic performance of high-speed train driving on tunnel-bridge section under fluctuating winds based on three turbulence models. J Wind Eng Ind Aerodyn, 2022, 228. 105081

[115] SterlingM, BakerC, BouferroukA, et al.. An investigation of the aerodynamic admittances and aerodynamic weighting functions of trains. J Wind Eng Ind Aerod, 2009, 97: 512-522.

[116] ZhuS, LiY, XuX. Wind tunnel test on the aerodynamic admittance of a rail vehicle in crosswinds. J Wind Eng Ind Aerodyn, 2022, 226. 105052

[117] BaoY, XiangH, LiY, et al.. Dynamic effects of turbulent crosswinds on a suspended monorail vehicle-curved bridge coupled system. J Vib Control, 2021, 28(9–10): 1135-1147

[118] YangY, HeQ, LiS, et al.. Dynamic features and wind-resistant strategy of suspended monorail vehicle–track beam systems subjected to turbulent wind. App Math Model, 2024, 137. 115696

[119] BaoY, ZhaiW, CaiC, et al.. Impact coefficient analysis of track beams due to moving suspended monorail vehicles. Veh Syst Dyn, 2022, 60(2): 653-669.

[120] BaoY, XiangH, LiY. A dynamic analysis scheme for the suspended monorail vehicle-curved bridge coupling system. Adv Struct Eng, 2020, 23(8): 1728-1738.

[121] CheliF, RipamontiF, RocchiD, et al.. Aerodynamic behavior investigation of the new EMUV250 train to cross wind. J Wind Eng Ind Aerod, 2010, 98(4–5): 189-201.

[122] ZhaiW, YangJ, ZhenL, et al.. Dynamics of high-speed train in crosswinds based on an air-train-track interaction model. Wind Struct, 2015, 20(2): 143-168.

[123] ZhuB, ZhangC, ZhangZ, et al.. Dynamic analysis of suspension-type monorail long-span cable-stayed bridge in a wind–vehicle–bridge system. Urban Rail Transit, 2023, 9: 19-30.

[124] HuB, PanY, LuZ, et al.. Construction practice of the first suspension monorail test line in China. Urban Rapid Rail Transit, 2019, 32(1): 38-42(in Chinese)

[125] HeQ, ZhaiW, ZhuS, et al.. Experimental research on dynamic performance of suspended monorail train–bridge coupled system. J China Railw Soc, 2018, 40(10): 57-63(in Chinese)

[126] GB/T 5599–2019. Specification for dynamic performance assessment and testing verification of rolling stock. Standards Press of China, Beijing, 2019 (in Chinese)

[127] DBJ51/T 099–2018. Standard for design of suspended monorail transit. Southwest Jiaotong University Press, Chengdu, 2018 (in Chinese)

Funding

National Natural Science Foundation of China(52202483)

RIGHTS & PERMISSIONS

The Author(s)