Analytical study on the dynamic displacement response of a curved track subjected to moving loads

Li, Kefei; Liu, Weining; Markine, Valéri; Han, Zhiwei

doi:10.1631/jzus.a1300225

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…In this work, trigonometric functions were employed as the trial functions to approximate the displacement of the curved rail. Li et al performed an analytical study of the dynamic response of a curved track subjected to moving loads, and presented a model of a curved Timoshenko beam periodically supported by double-layer spring-damping elements 15,16 . In this model, the displacement of the rail under moving loads is expressed as the product of the load and the transfer function for the curved track based on the Duhamel integral and the dynamic reciprocity theorem.…”

Section: Yang Et Al Established a Complete Theory For Treating The Vmentioning

confidence: 99%

“…The response at the excitation point is expressed as the mobility, that is the velocity due to a unit harmonic force. In addition the decay rates of vibration along the track are 16 determined. The vertical response at Position A and the lateral one at Position B on the rail head due to a vertical force applied at Point A or a lateral one at Point B (Fig.…”

Section: Mobility and Decay Rate Of The Track Due To Non-moving Harmomentioning

confidence: 99%

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Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory

Liu

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part F:

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The dynamic response of a curved railway track subjected to moving and non-moving harmonic loads is studied in this paper. The track is considered as a curved Timoshenko beam supported by periodically-spaced discrete fasteners. The displacement and rotation of the curved rail are expressed as the superposition of track modes in the frequency domain. Periodic structure theory is applied to the equations of motion of a curved track, allowing the dynamic response of the track to be calculated efficiently in a reference cell. The effect of the stiffness and damping of the fasteners, the fastener spacing and the radius of curvature on the mobility and decay rate of the track is analysed for non-moving loads on the rail head. The vibration of the rail under moving loads is also discussed. It is found that the dynamic response of a curved rail with a large radius has the same characteristics as that of a straight track. However, the dynamic response of the track is significantly affected when the radius of curvature becomes small. The radius affects the mobility, the decay rate below 2000 Hz and the velocity of the rail in the vertical direction when the radius is smaller than about 15 m and for the lateral direction when it is less than about 30 m. Moreover, the curvature has a significant influence on the vertical/lateral cross mobility, the magnitude of which increases as the radius is reduced. When the radius is larger than 10 m, the lateral vibration amplitude under a moving vertical load and the vertical response to a moving lateral load are inversely proportional to the radius.If the curved rail is supported by a continuous elastic foundation, the response of the rail can also be calculated. The forces applied on the rail by the fasteners in equations (7)-(12) can be replaced with product of the dynamic stiffness of the foundation and the displacement of the rail,

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Section: Yang Et Al Established a Complete Theory For Treating The Vmentioning

confidence: 99%

Section: Mobility and Decay Rate Of The Track Due To Non-moving Harmomentioning

confidence: 99%

Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory

Liu

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part F:

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“…Martínez-Casas et al (2014) developed a model for a flexible wheelset running on a flexible curved track. Based on the periodic structure theory, Li et al (2013) performed an analytical study on the dynamic responses of a curved track subjected to moving loads. Du et al (2017) and Liu et al (2018) proposed a model of a curved railway track subjected to harmonic loads, and the in-plane track vibration was considered and compared with the research performed by Li et al (2013).…”

Section: Introductionmentioning

confidence: 99%

“…To analyse the train-track dynamic problem for a curved line, Sun and Simson (2007) 2013) performed an analytical study on the dynamic responses of a curved track subjected to moving loads. Du et al (2017) and Liu et al (2018) proposed a model of a curved railway track subjected to harmonic loads, and the in-plane track vibration was considered and compared with the research performed by Li et al (2013). To investigate the ground vibration generated by trains in a curved tunnel, Shi et al (2018) performed an in situ measurement.…”

Section: Introductionmentioning

confidence: 99%

Prediction of building vibration induced by metro trains running in a curved tunnel

Du³

et al. 2020

Journal of Vibration and Control

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Curved metro lines currently account for a significant proportion of total route mileage. However, the existing prediction model of environmental vibration only considered the vibration induced by trains running in a straight tunnel. In the present study, a numerical model was proposed to predict the environmental vibration induced by trains running in a curved tunnel. The model was divided into two parts: a train–track coupled model and a tunnel–soil–building finite element model. In the first part, a novel three-dimensional train–curved track coupled model was established and solved in the frequency domain based on the periodic theory. Both vertical and horizontal train loads were calculated by this model. Then, an in situ measurement was performed in the curved tunnel of an operating metro line, and the tunnel vibration responses were obtained and used to calibrate the train–track model. Finally, a case study was selected from Beijing metro line 16, where it is needed to predict and evaluate the environmental impact of vibration from a curved metro line being planned for construction beneath an office building. A three-dimensional tunnel–soil–building finite element model was built, and the building vibrations in vertical and horizontal directions were predicted. The results show that the floor vibrations have peak values of approximately 5.29 and 27.8 Hz, which are exacerbated by the building local mode and the spacing of the rail supports. Below the third floor, the vertical vibration response exceeded the vibration control limit recommended by Chinese national standards. Track solutions for vibration control must be implemented to mitigate the environmental vibrations.

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Dynamic Analysis of Railway Track Response Subjected to Train Moving Loads Using Finite Element Simulation

Rhylane

Ajdour

2023

Transp. Infrastruct. Geotech.

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Analytical study on the dynamic displacement response of a curved track subjected to moving loads

Cited by 10 publications

References 15 publications

Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory

Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory

Prediction of building vibration induced by metro trains running in a curved tunnel

Dynamic Analysis of Railway Track Response Subjected to Train Moving Loads Using Finite Element Simulation

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