In this study, a half-space 13-degree-of-freedom vehicle model, a double track model, and a train-bridge interaction model were integrated to form a combined people-train-rail-bridge interaction model to analyze the vertical Sperling index of the train body and passengers as realistically as possible. In this bigger, more complete, and novel model, the separation between the vehicle and bridge is considered. By comparing measured data and simulated results obtained using the proposed model with the Newmark-Beta algorithm, the effectiveness of the model was verified, and the results demonstrated that these two values were very close. Upon further numerical analysis, the dynamic responses of the train and the three equivalent human bodies at different train speeds were computed using the developed vehicle-structure dynamic analysis program with different abruptness values in the random rail irregularities. The results of these four dynamic responses revealed that the rail irregularities affected the vertical acceleration of the three equivalent human bodies and train, and the best Sperling index evaluation standard for the train was not fixed (as assumed when only considering the train body) but varied with the passenger position as the train traveled over irregularities.
[1] ROMAN C, MARTIN J C. Integration of HSR and air transport: Understanding passengers’ preferences [J].Transportation Research Part E: Logistics and Transportation Review, 2014, 71: 129-141.
[2] ZHAI W M, ZHAO C F, XIA H, et al. Basic scientific issues on dynamic performance evolution of the highspeed railway infrastructure and its service safety [J]. Scientia Sinica (Technologica), 2014, 44(7): 645-660(in Chinese).
[3] YANG Y B, YAU J D, HSU L C. Vibration of simple beams due to trains moving at high speeds [J]. Engineering Structures, 1997, 19(11): 936-944.
[4] YAU J D, WU Y S, YANG Y B. Impact response of bridges with elastic bearings to moving loads [J]. Journal of Sound and Vibration, 2001, 248(1): 9-30.
[5] FRYBA L. A rough assessment of railway bridges for high speed trains [J]. Engineering Structures, 2001,23(5): 548-556.
[6] XIAO F, CHEN G S, HULSEY J L, et al. Characterization of nonlinear dynamics for a highway bridge in Alaska [J]. Journal of Vibration Engineering & Technologies, 2018, 6(5): 379-386.
[7] HUNG C F, HSU W L. Influence of long-wavelength track irregularities on the motion of a high-speed train[J]. Vehicle System Dynamics, 2018, 56(1): 95-112.
[8] LING L, ZHANG Q, XIAO X B, et al. Integration of car-body flexibility into train-track coupling system dynamics analysis [J]. Vehicle System Dynamics, 2018,56(4): 485-505.
[9] CUTINI M, BRAMBILLA M, BISAGLIA C. Assessment of a ride comfort number for agricultural tractors: A simplified approach [J]. Biosystems Engineering, 2019, 185: 35-44.
[10] CHANG K C, WU F B, YANG Y B. Disk model for wheels moving over highway bridges with rough surfaces [J]. Journal of Sound and Vibration, 2011,
330(20): 4930-4944.
[11] DENG L, CAI C S. Identification of parameters of vehicles moving on bridges [J]. Engineering Structures,2009, 31(10): 2474-2485.
[12] RAMALINGAM M, DAVIDSON JEBASEELAN D.The effect of vibration characteristics of an automotive seating system on ride comfort: A finite elemenstudy [J]. Proceedings of the Institution of Mechanical Engineers, Part C : Journal of Mechanical Engineering Science, 2019, 233(18): 6588-6601.
[13] JIANG P B, LING L, DING X, et al. Track irregularity sensitive wavelengths of high-speed railway considering flexible vibration of vehicle body [J]. Journal of Vibration and Shock, 2021, 40(15): 79-89.
[14] YOUCEF K, SABIHA T, MOSTAFA D, et al. Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities [J]. Journal of Mechanical Science and Technology, 2013, 27(4): 951-962.
[15] TOMIOKA T, TAKIGAMI T, SUZUKI Y. Numerical analysis of three-dimensional flexural vibration of railway vehicle car body [J]. Vehicle System Dynamics, 2006, 44(sup1): 272-285.
[16] TOMIOKA T, TAKIGAMI T. Experimental and numerical study on the effect due to passengers on flexural vibrations in railway vehicle carbodies [J]. Journal of Sound and Vibration, 2015, 343: 1-19.
[17] TOMIOKA T, TAKIGAMI T, AIDA K. Experimental investigations on the damping effect due to passengers on flexural vibrations of railway vehicle carbody and basic studies on the mimicry of the effect with simple substitutions [J]. Vehicle System Dynamics, 2017,55(7): 995-1011.
[18] HUI C, WEIHUA Z, MIAO B R. Vertical vibration analysis of the flexible carbody of high speed train [J].International Journal of Vehicle Structures and Systems, 2015, 7(2): 55-60.
[19] GONG D, ZHOU J S, SUN W J. Passive control of railway vehicle car body flexural vibration by means of underframe dampers [J]. Journal of Mechanical Science and Technology, 2017, 31(2): 555-564.
[20] DUMITRIU M. On the critical points of vertical vibration in a railway vehicle [J]. Archive of Mechanical Engineering, 2014, 61(4): 609-625.
[21] DUMITRIU M. A new passive approach to reducing the carbody vertical bending vibration of railway vehicles [J]. Vehicle System Dynamics, 2017, 55(11): 1787-1806.
[22] CHEN R, CHEN J Y, WANG P, et al. Impact of wheel profile evolution on wheel-rail dynamic interaction and surface initiated rolling contact fatigue in turnouts [J].Wear, 2019, 438/439: 203109.
[23] LIU X W, XIE J, WU C, et al. Semi-analytical solution of vehicle-bridge interaction on transient jump of wheel[J]. Engineering Structures, 2008, 30(9): 2401-2412.
[24] YANG Y B, YAU J D, WU Y S. Vehicle-bridge interaction dynamics - with applications to high-speed railways [M]. Singapore: World Scientific Publishing Co. Pte. Ltd., 2004.
[25] MADSHUS C, KAYNIA A M. High-speed railway lines on soft ground: Dynamic behaviour at critical train speed [J]. Journal of Sound and Vibration, 2000,231(3):689-701.
[26] HIRT M A. Eurocode 1: Basis of design and actions on structures [J]. Schweizer Ingenieur und Architekt, 1993(16/17): 273-275.
[27] LEBEL D, SOIZE C, FUNFSCHILLING C, et al. Sta-tistical inverse identification for nonlinear train dynamics using a surrogate model in a Bayesian framework [J]. Journal of Sound and Vibration, 2019, 458:158-176.
[28] WU C, LIU X W, HUANG X C. Alterable-element method for vehicle-bridge interaction considering the transient jump of wheel [J]. Journal of Shanghai Jiaotong University (Science), 2008, 13(3): 330-335.
[29] PERRIN G, DUHAMEL D, SOIZE C, et al. Quantification of the influence of the track geometry variability on the train dynamics [J]. Mechanical Systems and Signal Processing, 2015, 60/61: 945-957.
[30] LIU X D, WANG H X, SHAN Y C, et al. Construction of road roughness in left and right wheel paths based on PSD and coherence function [J]. Mechanical Systems and Signal Processing, 2015, 60/61: 668-677.
[31] XU L, ZHAI W M. A novel model for determining the amplitude-wavelength limits of track irregularities accompanied by a reliability assessment in railway vehicle-track dynamics [J]. Mechanical Systems and Signal Processing, 2017, 86: 260-277.
