Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities are studied in this paper. The rail irregularity is regarded as a random process. By extending the pseudo-excitation method, three kinds of rail irregularity are transformed into a pseudo load vector of the coupled system. A finite element model is used to describe the bridge and a spatial multi-body mass–spring–damping model is adopted to represent a moving railway car. Monte Carlo simulations are implemented to validate the presented method. A detailed case study on the train–bridge coupled system is conducted; it is focused on the effects of three kinds of rail irregularity on the stochastic characteristics of the dynamic responses of the system. The effect of randomness on the level of safety and the riding comfort created by the coupled system are also discussed. The results demonstrate that track irregularities may have a greater impact on the transverse response of the coupled system than on the vertical responses.
FrýbaL. Dynamics of railway bridges, 2nd ed. London, UK: Thomas Telford, 1996.
2.
FrýbaLPirnerM. Load tests and modal analysis of bridges. Engng Struct2001; 23(1): 102–109.
3.
FrýbaL. Effect of a force moving at variable speed along a beam. Acta Tech CSAV1973; 18(1): 54–68.
4.
LouP. A new three-dimensional finite element analysis model of high-speed train-bridge interactions. Engng Struct2004; 26(9): 1319–1320.
5.
XiaHZhangN. Dynamic analysis of railway bridge under high-speed trains. Comput Struct2005; 83(23–24): 1891–1901.
6.
LeeCHKimCWKawataniM. Dynamic response analysis of monorail bridges under moving trains and riding comfort of trains. Engng Struct2005; 27(14): 1999–2013.
7.
AuFWangJJCheungYK. Impact study of cable-stayed bridge under railway traffic using various models. J Sound Vib2001; 240(3): 447–465.
8.
WuYSYangYB. Steady-state response and riding comfort of trains moving over a series of simply supported bridges. Engng Struct2003; 25(2): 251–265.
9.
ChengYSAuFCheungYK. Vibration of railway bridges under a moving train by using bridge-track-vehicle element. Engng Struct2001; 23(12): 1597–1606.
10.
WangWYanWDengLKangH. Dynamic analysis of a cable-stayed concrete-filled steel tube arch bridge under vehicle loading. J Bridge Engng2014; 20(5): 04014082-1 -04014082-12.
11.
BradySO'BrienE. Effect of vehicle velocity on the dynamic amplification of two vehicles crossing a simply supported bridge. J Bridge Engng2006; 11(2): 250–256.
12.
ZhangYCaiCShiXWangC. Vehicle-induced dynamic performance of FRP versus concrete slab bridge. J Bridge Engng2006; 11(4): 410–419.
13.
NortonTRLashgariMMohseniM. Multimode dynamic response of railway bridge superstructures to high-speed train loads. Proc IMechE, Part F: J Rail Rapid Transit2014; 228(7): 744–758.
14.
XiaHChenJGXiaCY. An experimental study of train-induced structural and environmental vibrations of a rail transit elevated bridge with ladder tracks. Proc IMechE, Part F: J Rail Rapid Transit2010; 224(3): 115–124.
FrýbaL. Non-stationary response of a beam to a moving random force. J Sound Vib1976; 46(3): 323–338.
17.
RystwejASniadyP. Dynamic response of an infinite beam and plate to a stochastic train of moving forces. J Sound Vib2007; 299(4–5): 1033–1048.
18.
ŚniadyPBiernatSSieniawskaRŻukowskiS. Vibrations of the beam due to a load moving with stochastic velocity. Prob Engng Mech2001; 16(1): 53–59.
19.
Abu-HilalM. Dynamic response of a double Euler–Bernoulli beam due to a moving constant load. J Sound Vib2006; 297(3–5): 477–491.
20.
LuFGaoQLinJHWilliamsFW. Non-stationary random ground vibration due to loads moving along a railway track. J Sound Vib2006; 298(1–2): 30–42.
21.
AuFWangJJCheungYK. Impact study of cable-stayed railway bridges with random rail irregularities. Engng Struct2002; 24(5): 529–541.
22.
XiaHde RoeckGZhangHRZhangN. Dynamic analysis of train-bridge system and its application in steel girder reinforcement. Comput Struct2001; 79(20–21): 1851–1860.
23.
Jin ZB. Train-track-bridge system and train-bridge stochastic vibration. PhD Thesis, Southwest Jiaotong University, People's Republic of China, 2007.
24.
LinJZhaoYZhangY. Accurate and highly efficient algorithms for structural stationary/non-stationary random responses. Comput Method Appl Mech Engng2001; 191(1–2): 103–111.
25.
ZengZYuZZhaoY. Numerical simulation of vertical random vibration of train-slab track-bridge interaction system by PEM. Shock Vib2014. 1–21.
26.
LuFLinJHKennedyDWilliamsFW. An algorithm to study non-stationary random vibrations of vehicle-bridge systems. Comput Struct2009; 87(3–4): 177–185.
27.
Karis T. Track irregularities for high-speed trains. Master's Thesis, KTH Royal Institute of Technology, Sweden, 2009.
28.
SongMNohHChoiC. A new three-dimensional finite element analysis model of high-speed train–bridge interactions. Engng Struct2003; 25(13): 1611–1626.
29.
YauJYangYKuoS. Impact response of high speed rail bridges and riding comfort of rail cars. Engng Struct1999; 21(9): 836–844.
30.
XiaHZhangN. Dynamic interaction of vehicles and structures, Beijing, People's Republic of China: Science Press, 2005. .
31.
LinJHZhangYH. Pseudo excitation method in random vibration, Beijing, People's Republic of China: Science Press, 2006.
