Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method

Abstract

A method for analysing the vehicle–bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities (PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel–rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors (derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.

Keywords

Vehicle–bridge interaction system / Pseudo-excitation method (PEM) / Derailment coefficient / Wheel unloading rate / Lateral wheel axle force / Probability density function

References

[1.] Zhai W Han Z Chen Z . Train–track–bridge dynamic interaction: a state-of-the-art review. Veh Syst Dyn, 2019 57 984-1027

[2.] Zhai W Xia H Cai C . High-speed train–track–bridge dynamic interactions, part I: theoretical model and numerical simulation. Int J Rail Transp, 2013 1 1–2 3-24

[3.] Garcia-Palacios SA Melis M. Analysis of the railway track as a spatially periodic structure. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2018 226 2 113-123

[4.] Perrin G Soize C Duhamel D . Track irregularities stochastic modeling. Probabilist Eng Mech, 2013 34 123-130

[5.] Wetzel C Proppe C. Stochastic modeling in multibody dynamics: aerodynamic loads on ground vehicles. J Comput Nonlin Dyn, 2010 5 3 470-478

[6.] Majka M Hartnett M. Dynamic response of bridges to moving trains: a study on effects of random track irregularities and bridge skewness. Comput Struct, 2009 87 19–20 1233-1252

[7.] Wu SQ Law SS. Statistical moving load identification including uncertainty. Probabilist Eng Mech, 2012 29 70-78

[8.] Lombaert G Conte JP. Random vibration analysis of dynamic vehicle–bridge interaction due to road unevenness. J Eng Mech, 2011 138 7 816-825

[9.] Kiureghian AD Neuenhofer A. Response spectrum method for multi-support seismic excitations. Earthq Eng Struct D, 2010 21 8 713-740

[10.] Alduse BP Jung S Vanli OA . Effect of uncertainties in wind speed and direction on the fatigue damage of long-span bridges. Eng Struct, 2015 100 468-478

[11.] Lin JH Zhao YH Zhao Y. Pseudo excitation method and some recent developments. Procedia Eng, 2011 14 2453-2458

[12.] Zhang YW Zhao Y Zhang YH. Riding comfort optimization of railway trains based on pseudo-excitation method and symplectic method. J Sound Vib, 2013 332 21 5255-5270

[13.] Zhu Z Wang L Pedro AC . An efficient approach for prediction of subway train-induced ground vibrations considering random track unevenness. J Sound Vib, 2019 455 459-479

[14.] Li X, Zhu Y, Jin Z (2016) Nonstationary random vibration performance of train–bridge coupling system with vertical track irregularity. Shock Vib 2016:1–19

[15.] Zhu Y Li X Jin Z. Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2016 230 8 1851-1876

[16.] Zhang ZC Lin JH Zhang YH. Non-stationary random vibration analysis for train–bridge systems subjected to horizontal earthquakes. Eng Struct, 2010 32 3571-3582

[17.] He XH Shi K Wu T. An efficient analysis framework for high-speed train–bridge coupled vibration under nonstationary winds. Struct Infrastruct E, 2020 16 9 1326-1346

[18.] Lei XY Noda NA. Analysis of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile. J Sound Vib, 2002 258 1 147-165

[19.] Zhang N Xia H. Dynamic analysis of coupled vehicle–bridge system based on inter-system iteration method. Comput Struct, 2013 114–115 26-34

[20.] Liu K Lombaert G De Roeck G. Dynamic analysis of multispan viaducts with weak coupling between adjacent spans. J Bridge E, 2014 19 1 83-90

[21.] Mohammadzadeh S Sangtarashha M Molatefi H. A novel method to estimate derailment probability due to track geometric irregularities using reliability techniques and advanced simulation methods. Arch Appl Mech, 2011 81 11 1621-1637