Nonstationary Random Vibration Performance of Train-Bridge Coupling System with Vertical Track Irregularity

Abstract

In order to study the random vibration performance of trains running on continuous beam bridge with vertical track irregularity, a time-domain framework of random analysis on train-bridge coupling system is established. The vertical rail irregularity is regarded as a random process. A multibody mass-spring-damper model is employed to represent a moving railway car and the bridge system is simulated by finite elements. By introducing the pseudo excitation algorithm into the train-bridge interaction dynamic system, expressions of the mean value, standard deviation, and power spectral density of the nonstationary random dynamic responses of bridge and vehicles are derived. Monte-Carlo simulations are implemented to validate the presented method. A comprehensive analysis of the train-bridge coupling system with vertical track irregularity is conducted focusing on the effect of the randomness of the vertical rail irregularity on the dynamic behavior of the running train and the three-span continuous concrete bridge. Moreover, stochastic characteristics of the indicator for assessing the safety and the riding quality of the railway cars running on continuous beam bridge are carried out, which may be a useful reference in the dynamic design of the bridge.

Application of KLE-PEM for Random Dynamic Analysis of Nonlinear Train-Track-Bridge System

“…Track irregularity can be measured using the railway line [9] and can also be obtained by converting the existing PSD function into spatial samples. Power spectrum simulation is used to obtain irregularity samples, where German lowinterference PSD is used [12]. 10,000 irregularity samples with 1,000 meters are obtained using the trigonometric series method [8] and utilized as the initial sample.…”

“…To obtain an efficient and accurate calculation method for the random dynamics of the TTBS, many studies have been conducted. For instance, the pseudo-excitation method was used for the random dynamics analysis of the train-track system and TTBS [12][13][14][15][16]. It is convenient to use the pseudo-excitation method for response power spectrum calculation in both nonstationary and stationary random excitation structural analysis with a high application value.…”

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

“…Zhu et al [13] proposed an approach for predicting the train-induced ground vibrations considering random track unevenness. Li et al [14] and Zhu et al [15] proved that the bridge responses follow Gaussian distributions and established a framework to calculate the upper and lower limits of vehicle-bridge system responses from the auto-spectra and the cross-spectra of bridge vibrations.…”

“…He et al [17] proposed an efficient analysis framework for the interaction system subjected to wind loads and studied the nonstationary effects on the vibration responses. The methods presented in [10][11][12][13][14][15][16] were all validated by Monte Carlo simulations. By the above-mentioned studies, the statistic characteristics of response in frequency domain can be fully obtained, free of the accidental effect; also the dynamic behaviour in each frequency band of the system movements and forces can be obtained.…”

A Probabilistic Assessment Model for Train‐Bridge Systems: Special Attention on Track Irregularities

“…For example, Chatterjee et al [13], Au et al [14], Xia et al [15], and Liu et al [16,17] used multiple samples of track irregularities from one PSD to explore the effects of the location of irregularity amplitudes on system responses. By applying the pseudoexcitation method (PEM), researchers can efficiently study the random vibrations of train-bridge systems, where random irregularities were transformed into the superposition of a series of deterministic pseudoharmonic signals [18][19][20][21]. Rocha et al [22,23] took the assumption that the track spectra are uniformly distributed and employed the Monte Carlo simulation and tail modelling technique to assess the track stability caused by excessive deck vibrations and running safety of trains for a short-span railway bridge.…”