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To study the influence of the Chinese high-speed railway ballastless track spectrum and the German low-interference spectrum on riding comfort, a long-span highway-railway suspension bridge is studied as an example, and a passenger–train–bridge coupling model is established based on the structural dynamics. The vibration responses of the passenger–train–bridge system during the CRH2C train running on the bridge are studied by a combination of the self-written computer program and general finite element software, considering the hunting movement, and the riding comfort of trains and passengers is evaluated using $N_{\mathrm{\text{MV}}}$ and ISO-2631 standard, respectively. The results show that track irregularity has a few effects on the lateral vibration of the bridge. Compared with the German low-interference spectrum, the Chinese high-speed railway ballastless track spectrum has less exciting effects on the vibration of the passenger–train–bridge system and better riding comfort. Passengers in the middle of the train and on the middle seats of the same train have better riding comfort, and with the increase of train speed, the riding comfort of passengers will gradually reduce. Instead of passenger responses, the riding comfort classification based on the car body is overestimated.

This paper presents a non-stationary random vibration analysis of railway bridges under moving heavy-haul trains by the pseudo-excitation method (PEM) considering the train-track-bridge coupling dynamics. The train and the ballasted track-bridge are modeled by the multibody dynamics and finite element (FE) method, respectively. Based on the linearized wheel-rail interaction model, the equations of motion of the train-ballasted track-bridge coupling system are then derived. Meanwhile, the excitations between the rails and wheels caused by the random track irregularity are transformed into a series of deterministic pseudo-harmonic excitation vectors by the PEM. Then, the random vibration responses of the coupling system are obtained using a step-by-step integration method and the maximum responses are estimated using the 3$\sigma$ rule for the Gaussian stochastic process. The proposed method is validated by the field measurement data collected from a simply-supported girder bridge (SSB) for heavy-haul trains in China. Finally, the effects of train speed, grade of track irregularity, and train type on the random dynamic behavior of six girder bridges for heavy-haul railways are investigated. The results show that the vertical acceleration and dynamic amplification factor (DAF) of the midspan of the SSB girders are influenced significantly by the train speed and track irregularity. With the increase in the vehicle axle-load, the vertical deflection-to-span ratio ($\gamma$) of the girders increases approximately linearly, but the DAF and vertical acceleration fail to show clear trend.

The high-speed maglev vehicle-guideway coupled system (MVGCS) is a complex system, whose random vibration characteristics have not been well studied due to a limited number of examples. To address this issue, a new efficient approach is proposed for the random vibration analysis of the MVGCS, which combines the probability density evolution method and multi-time step method with multiple random loads considered. The random model established for 10-degree-of-freedom maglev vehicles and guideway is time-dependent, considering two different supporting conditions. The Monte Carlo method is used to assess the accuracy and efficiency of the proposed approximate approach, and the random model is verified through comparison with available results. The stochastic dynamic responses of the vehicles, guideway, and electromagnetic levitation forces, including the mean values and standard deviations, are determined in a case study. The results show that the proposed method is feasible for the dynamic analysis of maglev systems with a reasonably good efficiency in computation. Furthermore, critical parametric analyses involving vehicle speed, irregularity, and cut-off wavelength are performed with the results discussed.

The influence of track irregularity and deck deformation on the running safety of high-speed railway (HSR) trains is investigated, with emphasis placed on those caused by the creep of continuous prestressed bridges. A bridge model is established with CRTS II ballastless track to account for a train-track-bridge (TTB) system. The creep effect is calculated by the finite element software MIDAS/Civil. The accuracy of the numerical simulation is confirmed by comparing the numerical predictions with field measurements. Considering the stability index of the moving train, the deformation threshold for safe operation of the train is determined. The results show that the initial prestressing stress has a great impact on the residual deformation of the bridge, but the deformation of the rail is less affected by the stiffness of the fastener. Creep irregularity has a great influence on the comfort of the moving train, but does not affect its running safety. When the creep amplitude is greater than 4mm, the increase in the amplitude of the creep irregularity has a greater effect on the acceleration of the car body.

The dynamic interaction between the vehicle and track is one of the most critical issues for railways, as it is closely related to running safety. Previously, many vehicle–track coupling models have been developed to study the vibration response of the system. Even though the track is periodic and infinitely extended, only a finite length of the track has often been used in the simulation, so as to reduce the effort of computation. For some special issues, it is necessary to consider the influence of long-wavelength track irregularities on the vehicle responses, and the characteristic track length can reach up to the scale of kilometer. In practice, the computational effort of using a model to accommodate kilometer-long tracks is costly and even unacceptable. To overcome this problem, this paper proposes a novel snake-like model inspired by the famous game Snake to simulate infinite tracks. In the snake-like model, each vehicle can travel on the track repeatedly via the transfer nodes installed at the end of the track. Two examples were presented to verify the accuracy and efficiency of the model proposed. The results showed that the accuracy of snake-like model is consistent with that of existing methods, but the computational effort has been reduced significantly.

Railway transportation, as an important lifeline during earthquake relief and post-disaster reconstruction, has an extremely significant role. The study of track irregularity caused by earthquakes is the basis for ensuring traffic safety after their occurrence. In this paper, a finite element model of a five-span simply supported high-speed railway beam bridge with the China Railway Track System (CRTS) II was established and an experimental verification was performed. Eighty arbitrarily selected seismic waves were extracted from the Pacific Earthquake Engineering Research Center (PEER) strong ground motion database and a nonlinear time-history analysis was performed on the finite element model. The frequency–domain distribution law of earthquake-induced track irregularities was studied. A stable target earthquake-induced track irregularity spectrum model was constructed, and its expression was fitted. According to the results, in the case of transverse earthquakes, the rails experienced noticeable alignment irregularity and cross-level irregularity, while the amplitude of the gauge and vertical irregularity were relatively small. The target irregularity spectrum has a higher amplitude in the low-frequency components. When peak ground acceleration (PGA) was low, earthquake-induced track irregularity was not obvious, but the deteriorating effects of earthquakes on track irregularities increased significantly with increasing PGA.

A significant resonance pattern at high frequencies around 400Hz to 1000Hz has been well observed from measured rail accelerations. Such resonances are key issues for rail noise and corrugation. Although this pattern has been noted and discussed in various papers in terms of wave reflections among multiple wheels, the aim of this study is to develop novel dynamic model and reveal generation mechanism of this resonance phenomenon with the train-track coupled system. An infinite Timoshenko beam with continuous supports is adopted for modeling the track system, and the point and transfer receptances of the rail for a moving excitation are explicitly deduced by the residue theorem together with a Fourier transform-based method. A frequency-domain method is then established to calculate the power spectral densities (PSD) of the train-track coupled system responses to stochastic irregularities with the moving vehicle model with multiple wheels. It is found that the high-frequency resonances occur when the reflected waves generated from multiple wheels on the rail are exactly in phase with the initial track irregularity. The load speed has negligible influence on the wheel–rail interaction in the lower frequency range and a small influence in the upper frequency range only for very high train speeds.

The construction of high-speed railways continues to extend in seismic prone areas, but there is limited research on the seismic-induced track irregularities occurred in positions where high-speed railway bridges are involved. Taking a five-span high-speed railway simply supported beam bridge as the engineering example, the corresponding nonlinear system model, with CRTS II slab ballastless track, is established by using ANSYS finite element analysis software. The distribution mode of post-earthquake track residual irregularity is studied, the statistical characteristics of its power spectral density are analyzed, and a representative seismic-induced track geometric irregularity spectrum is constructed. The effects of the site categories and the epicenter distance on seismic-induced track spectrum are also discussed. The results show that after the earthquake, the alignment irregularity is significant, while the vertical, cross-level and gauge irregularities can be ignored. The amplitude of track geometric irregularity, caused by earthquake, increases significantly with the increase of ground motion intensity. The seismic-induced track spectrum obeys lognormal distribution at all frequencies. The track spectra almost coincide for all five site categories, thus, the impact of site categories on the seismic-induced track spectrum of high-speed railway bridges is considered negligible. Due to the pulse effect, the seismic-induced track spectrum of near-field earthquakes is significantly larger than that of far-field earthquakes.

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

This study proposes a method for assessing the effect of stochastic vibrations resulting from track irregularities which are rarely studied but significant on bridge fatigue. First, the pseudo-excitation method is utilized to determine the power spectrum density of stress. Subsequently, the trigonometric series method is employed to acquire the stress time history set. Then, a traditional fatigue life calculation method is employed for analysis. By utilizing a post-sampling method, the need for costly repetitive solutions of the vehicle-bridge coupling system is eliminated. Numerical simulations are conducted on a steel truss bridge, revealing the non-negligible effect of track irregularity on bridge fatigue performance. The study investigates the underlying mechanism, highlighting the pronounced influence of long-wave track irregularity. Moreover, the research explores the correlation between track smoothness and bridge fatigue performance, demonstrating that a decrease in track smoothness leads to an increase in fatigue loss. These findings emphasize the necessity of considering stochastic vibrations when evaluating bridge fatigue, providing valuable insights for bridge design and maintenance.

In this paper, a computational study using the moving element method (MEM) was carried out to investigate the dynamic response of a high-speed train–track system. Results obtained using Hertz contact model and linearized Hertz contact model are compared and discussed. The dynamic responses of a train travelling across a uniform foundation and a transition region are also investigated. Parametric study is performed to understand the effect of various factors on the occurrence and patterns of the jumping wheel phenomenon such as the variation of foundation stiffness, travelling speed of the train and the severity of railhead roughness.

The requirements for inspection and management of track irregularity have to be more rigorous due to safety and serviceability concerns as the increment of the train speed of high-speed train. The wavelength of track irregularity significantly affects running safety and riding comfort. To improve inspection, operation, efficiency, and address, the inability of the mid-chord offset method currently used on track inspection cars to identify some irregularity wavelengths, a measurement and assessment method is presented in this paper. Nonstationary and nonlinear vehicle dynamic response data caused by irregularities were measured by accelerometers mounted on the axle-box of a vehicle. The Hilbert–Huang transform (HHT) technique was applied to analyze the data. Components of specific irregularity wavelength could be effectively identified and accurately matched to the data measured by the track inspection car. Additionally, to obtain the complete waveform of the track irregularity, we propose a restoration method of track irregularity that combines the characteristics of the measurement magnification in the chord-based measuring system and the HHT signal-processing techniques.