# Vibration and Derailment Analyses of Trains Moving on Curved and Cant Rails
## 1 Introduction  
High-speed rail and mass rapid transit have become important transportation modes on a global scale, so safety and passenger comfort need to be taken seriously, especially in the case of curved railway systems. The vibration and derailment behavior of trains moving on curved rails are much more complicated than those on straight line rails. Thus, investigation of moving trains on curved rails is an important issue. There have been a number of studies on the interaction between wheels and curved rails, and these studies have increased in number in recent years. [PERSON] presented a detailed model for high-frequency wheel/rail interaction during curving under constant friction in the time domain, and the results from the interaction model were in good qualitative agreement with previously published findings on curve squeal [1]. [PERSON] et al. performed a vehicle-rail dynamics analysis of trains traveling at high speed on a curved or straight bridge, and they used the finite element method (FEM) to model vehicle and bridge subsystems coupled by contact forces [2]. [PERSON] et al. established a vehicle-rail model, where the paper focuses on the effects of frequent earthquakes on a vehicle on horizontally curved railways [3]. [PERSON] et al. proposed a three-dimensional (3D) vehicle-rail analysis method to study the resonant behavior of a vehicle-rail system, and they numerically elucidated the conditions for generating and canceling resonance [4]. [PERSON] et al. developed a time domain simplified model to study the effect of control measures on wheel/rail noise when the vehicle curves, while the effectiveness of resilient wheel and embedded track to control curve squeal noise were assessed [5]. [PERSON] et al. proposed a seismic vehicle-rail analysis method that can simulate different wheel-rail contact states, such as wheel detachment and wheelset derailment [6]. [PERSON] et al. evaluated the transient effectof curve radii on the possible occurrence of lateral track resonances, while curved track models in 3D space were developed using a commercial finite element package [7]. [PERSON] at al. proposed a curved 2.5D finite element method to model a tunnel-soil system in order to provide an appropriate artificial boundary for the computation domain, while a 2.5D analytical method considering the longitudinal, transverse, vertical, and rotational motions of a rail was developed to model a curved track [8]. [PERSON] et al. implemented a cargo-wagon-rail coupling model that adopts diagonal lashing to restrain cargo movement, where a preliminary dynamic simulation analysis demonstrated that the selected cargo tilted when the wagon negotiated curves [9]. [PERSON] and [PERSON] proposed a finite element model to simulate wheel-rail frictional rolling, where wheel-rail squeal-exciting contact was investigated with considerations of unsteady lateral creepage, velocity-dependent friction, and curved rails [10]. [PERSON] et al. developed a 3D coupled train-track-soil interaction model based on the multi-body simulation principle and finite element modeling theory, and this model was validated by comparing numerical results with experimental results in a good agreement [11]. [PERSON] et al. proposed a numerical model to predict the environmental vibration induced by trains running through a curved tunnel, and a three-dimensional (3D) train-curved track coupled model was established and solved in the frequency domain based on the periodic theory [12]. [PERSON] et al. studied the ambient vibration responses induced by the operation of a metro train on curved rail segments using a finite element method model. The results showed that the horizontal vibration induced by a metro train on curved segments cannot be ignored [13]. [PERSON] et al. studied the instability mechanisms in a constant friction coefficient situation, where a stability analysis of the wheel/rail contact dynamics in a curve was performed by using an equivalent point contact model combined with wheel and rail modal bases.