Response of train-bridge system under intensive seismic excitation by random vibration method

Abstract

Earthquake is a kind of sudden and destructive random excitation in nature. It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation, the intensity of which is larger than 7, acts in train-bridge system. Firstly, the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established, where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom, while the single-span simple supported bridge subsystem is composed of 10 2D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support. Secondly, Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system. The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method, respectively solved by precise integral method and Newmark-β method through the inter-system iterative procedure. Finally, the results are compared with the case under the weak seismic excitation, and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution. In a high probability, the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.

Keywords

random vibration method / intensive seismic excitation / train-bridge system / probability distribution / intersystem iteration / precise integral method

References

[1] O’PeillyG J. Seismic intensity measures for risk assessment of bridges [J]. Bulletin of Earthquake Engineering, 2021, 19(9): 3671-3699

[2] YauJ D, FrýbaL. Response of suspended beams due to moving loads and vertical seismic ground excitations [J]. Engineering Structures, 2007, 29(12): 3255-3262

[3] YauJ D. Dynamic response analysis of suspended beams subjected to moving vehicles and multiple support excitations [J]. Journal of Sound and Vibration, 2009, 325(4–5): 907-922

[4] NishimuraK, TerumichiY, MorimuraT, et al.. Experimental study on the vehicle safety by earthquake track excitation with 1/10 scale vehicle and roller rig [J]. Journal of System Design and Dynamics, 2010, 4(1): 226-238

[5] NishimuraK, TerumichiY, MorimuraT, et al.. Analytical study on the safety of high speed railway vehicle on excited tracks [J]. Journal of System Design and Dynamics, 2010, 4(1): 211-225

[6] HeX-W, KawataniM, HayashikawaT, et al.. Numerical analysis on seismic response of Shinkansen bridge-train interaction system under moderate earthquakes [J]. Earthquake Engineering and Engineering Vibration, 2011, 10(1): 85-97

[7] LohC H, LeeZ-K. Seismic monitoring of a bridge: Assessing dynamic characteristics from both weak and strong ground excitations [J]. Earthquake Engineering & Structural Dynamics, 1997, 26(2): 269-288

[8] QiJ-J, JiangL-Z. Experimental study on seismic behaviors of steel-concrete composite frames [J]. Journal of Central South University, 2015, 22(11): 4396-4413

[9] ZhuZ-H, GongW, WangK, et al.. Dynamic effect of heavy-haul train on seismic response of railway cable-stayed bridge [J]. Journal of Central South University, 2020, 27(7): 1939-1955

[10] LinJ-H, ZhangW-S, WilliamsF W. Pseudoexcitation algorithm for nonstationary random seismic responses [J]. Engineering Structures, 1994, 16(4): 270-276

[11] ZhangZ C, LinJ H, ZhangY H, et al.. Nonstationary random vibration analysis of coupled vehicle-bridge systems [J]. Engineering Computations, 2010, 27(6): 712-732

[12] HeX-H, ShiK, WuT. An efficient analysis framework for high-speed train-bridge coupled vibration under non-stationary winds [J]. Structure and Infrastructure Engineering, 2020, 16(9): 1326-1346

[13] ZhuS-Y, LiY-L. Random characteristics of vehicle-bridge system vibration by an optimized pseudo excitation method [J]. International Journal of Structural Stability and Dynamics, 2020, 20(5): 2050069

[14] YuH-L, WangB, XiaC-P, et al.. Efficient non-stationary random vibration analysis of vehicle-bridge system based on an improved explicit time-domain method [J]. Engineering Structures, 2021, 231111786

[15] XiaH, ZhangN, GuoW-WDynamic interaction of train-bridge systems in high-speed railways [M], 2018, Berlin, Heidelberg, Springer Berlin Heidelberg

[16] BATHE K J. Finite element procedures [M]. Prentice Hall, Pearson Education, Inc, 2006.

[17] ArgentiniT, PaganiA, RocchiD, et al.. Monte Carlo analysis of total damping and flutter speed of a long span bridge: Effects of structural and aerodynamic uncertainties [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2014, 12890-104

[18] BogdanoffJ L, GoldbergJ E, BernardM C. Response of a simple structure to a random earthquake-type disturbance [J]. Bulletin of the Seismological Society of America, 1961, 51(2): 293-310

[19] LinJ H, ZhangY H, LiQ S, et al.. Seismic spatial effects for long-span bridges, using the pseudo excitation method [J]. Engineering Structures, 2004, 26(9): 1207-1216

[20] ZhongW-X, CaiZ-Q. Precise integration method for LQG optimal measurement feedback control problem [J]. Applied Mathematics and Mechanics, 2000, 21(12): 1417-1422

[21] TB10621—2014. Code for design of high-speed railway [S]. China Railway Publishing House. (in Chinese)

[22] ZhangN, XiaH. A vehicle-bridge interaction dynamic system analysis method based on inter-system iteration [J]. China Railway Science, 2013, 34(5): 32-38(in Chinese)

[23] HorováI, KoláčekJ, ZelinkaJKernel smoothing in Matlab [M], 2012, Singapore, World Scientific

[24] ZghoulA A. A goodness of fit test for normality based on the empirical moment generating function [J]. Communications in Statistics-Simulation and Computation, 2010, 39(6): 1292-1304

[25] RofooeiF R, MobarakeA, AhmadiG. Generation of artificial earthquake records with a nonstationary Kanai-Tajimi model [J]. Engineering Structures, 2001, 23(7): 827-837

[26] XiangJ, LiD-J, ZengQ-Y. Simulation of spatially coupling dynamic response of train-track time-variant system [J]. Journal of Central South University of Technology, 2003, 10(3): 226-230

[27] LiuC, ThompsonD, GriffinM J, et al.. Effect of train speed and track geometry on the ride comfort in highspeed railways based on ISO 2631-1 [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2020, 234(7): 765-778