Numerical analysis of moving train induced vibrations on tunnel,surrounding ground and structure

This study is focused on the effect of vibration induced by moving trains in tunnels on the surrounding ground and structures.A three-dimensional finite element model is established for a one-track railway tunnel and an adjacent twelve-storey building frame by using commercial software Midas GTS-NX(2019)and Midas Gen.This study considered the moving load effect of a complete train,which varies with space as well as with time.The effect of factors such as train speed,overburden pressure on the tunnel and variation in soil properties are studied in the time domain.As a result,the variations in horizontal and vertical acceleration for two different sites,i.e.,the free ground surface(without structure)and the area containing the structure,are compared.Also,the displacement pattern of the raft foundation is plotted for different train velocities.At lower speeds,the heaving phenomenon is negligible,but as the speed increases,both the heaving and differential settlement increase in the foundation.This study demonstrates that the effect of moving train vibrations should be considered in the design of new nearby structures and proper ground improvement should be considered for existing structures.

Torque effect on vibration behavior of high-speed train gearbox under internal and external excitations

The high-speed train transmission system,experiencing both the internal excitation originating from gear meshing and the external excitation originating from the wheel-rail interaction,exhibits complex dynamic behavior in the actual service environment.This paper focuses on the gearbox in the high-speed train to carry out the bench test,in which various operat-ing conditions(torques and rotation speeds)were set up and the excitation condition covering both internal and external was created.Acceleration responses on multiple positions of the gearbox were acquired in the test and the vibration behavior of the gearbox was studied.Meanwhile,a stochastic excitation modal test was also carried out on the test bench under different torques,and the modal parameter of the gearbox was identified.Finally,the sweep frequency response of the gearbox under gear meshing excitation was analyzed through dynamic modeling.The results showed that the torque has an attenuating effect on the amplitude of gear meshing frequency on the gearbox,and the effect of external excitation on the gearbox vibration cannot be ignored,especially under the rated operating condition.It was also found that the torque affects the modal param-eter of the gearbox significantly.The torque has a great effect on both the gear meshing stiffness and the bearing stiffness in the transmission system,which is the inherent reason for the changed modal characteristics observed in the modal test and affects the vibration behavior of the gearbox consequently.

Retrospective study of effect of whole-body vibration training on balance and walking function in stroke patients

BACKGROUND Dysfunction in stroke patients has been a problem that we committed to solve and explore.Physical therapy has some effect to regain strength,balance,and coordination.However,it is not a complete cure,so we are trying to find more effective treatments.AIM To observe the effect of whole-body vibration training(WVT)on the recovery of balance and walking function in stroke patients,which could provide us some useful evidence for planning rehabilitation.METHODS The clinical data of 130 stroke participants who underwent conventional rehabilitation treatment in our hospital from January 2019 to August 2020 were retrospectively analyzed.The participants were divided into whole-body vibration training(WVT)group and non-WVT(NWVT)group according to whether they were given WVT.In the WVT group,routine rehabilitation therapy was combined with WVT by the Galileo Med L Plus vibration trainer at a frequency of 20 Hz and a vibration amplitude of 0+ACY-plusmn+ADs-5.2 mm,and in the NWVT group,routine rehabilitation therapy only was provided.The treatment course of the two groups was 4 wk.Before and after treatment,the Berg balance scale(BBS),3 m timed up-and-go test(TUGT),the maximum walking speed test(MWS),and upper limb functional reaching(FR)test were performed.RESULTS After 4 wk training,in both groups,the BBS score and the FR distance respectively increased to a certain amount(WVT=46.08±3.41 vs NWVT=40.22±3.75;WVT=20.48±2.23 vs NWVT=16.60±2.82),with P<0.05.Furthermore,in the WVT group,both BBS score and FR distance(BBS:18.32±2.18;FR:10.00±0.92)increased more than that in the NWVT group(BBS:13.29±1.66;FR:6.16±0.95),with P<0.05.Meanwhile,in both groups,the TUGT and the MWS were improved after training(WVT=32.64±3.81 vs NWVT=39.56±3.68;WVT=12.73±2.26 vs NWVT=15.04±2.27,respectively),with P<0.05.The change in the WVT group(TUGT:17.49±1.88;MWS:6.79±0.81)was greater than that in the NWVT group(TUGT:10.76±1.42;MWS:4.84±0.58),with P<0.05.CONCLUSION The WVT could effectively improve the balance and walking function in stroke patients,which may be good for improving their quality of life.

The Progress of the Study on the Effect of Vibration Training on Muscle Strength Exercise

Vibration training is more and more extensively applied to the field of strength training. It, as a beneficial supplement to the traditional strength, is able to improve specific strength or the strength of weak positions, for the purpose of achieving the muscle strength development in an all-round way. In this paper, the anatomy, physiology, and biomechanics foundations for vibration training to increase muscle strength are mainly analyzed, and then the principle of vibration training to increase muscle strength is further expounded, and also the increase of muscle strength is discussed from the aspects such as vibration frequency, vibration amplitude, vibration posture, vibration intermittent time, and vibration mode, so as to clarify the domestic and foreign progress of the study on vibration training.

Seismic features of vibration induced by train

Based on schematically formulation of the vibrations induced by moving trains, this paper analyses the waveforms along the Datong-Qinhuangdao railroad in Northern China recorded in the suburban Huairou district of Beijing on March 8, 2003. It is illustrated that vibrations induced by train, except traditional recognized noises and interfer- ence effects, could be used as a seismic source to detect crustal structures with its advantage of abundant frequency spectrum, repeatability and no additional harm to the environment. It will bring lights to the traditional exploration seismology with the further studies of signal processing and interpretation methods, and related models and new observing systems.

Experimental investigation of railway train-induced vibrations of surrounding ground and a nearby multi-story building

In this paper, a field experiment was carried out to study train-induced environmental vibrations. During the field experiment, velocity responses were measured at different locations of a six-story masonry structure near the Beijing- Guangzhou Railway and along a small road adjacent to the building. The results show that the velocity response levels of the environmental ground and the building floors increase with train speed, and attenuate with the distance to the railway track. Heavier freight trains induce greater vibrations than lighter passenger trains. In the multi-story building, the lateral velocity levels increase monotonically with floor elevation, while the vertical ones increase with floor elevation in a fluctuating manner. The indoor floor vibrations are much lower than the outdoor ground vibrations. The lateral vibration of the building along the direction of weak structural stiffness is greater than along the direction with stronger stiffness. A larger room produces greater floor vibrations than the staircase at the same elevation, and the vibration at the center of a room is greater than at its corner. The vibrations of the building were compared with the Federal Transportation Railroad Administration （FTA） criteria for acceptable ground-borne vibrations expressed in terms ofrms velocity levels in decibels. The results show that the train-induced building vibrations are serious, and some exceed the allowance given in relevant criterion.

Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.

Field experiment of subgrade vibration induced by passing train in a seasonally frozen region of Daqing

The vibration characteristics and attenuation of the subgrade caused by passing trains in a seasonally frozen region of Daqing, China are investigated. Three field experiments were conducted during different times through the year, in normal, freezing and thawing periods, respectively, and the influence of the season, train speed and train type, is described in this paper. The results show that： （1） the vertical component is the greatest among the three components of the measured vibration near the rail track, and as the distance to the railway track increases, the dominant vibration depends on the season. （2） Compared with the vibration in the normal period, the vertical and longitudinal vibrations increase while the lateral vibration decreases in the freezing period. However, in the thawing period, the vertical and longitudinal vibrations decrease, and the lateral vibration increases. （3） As train speeds increase, the subgrade vibration increases. （4） The vibration induced by a freight train is greater than by a passenger train. These observations provide a better understanding of the vibration and dynamic stability of the subgrade and may be useful in developing criteria for railway and building construction in cold regions.

Seismic features of vibration induced by train

Based on schematically formulation of the vibrations induced by moving trains, this paper analyses the waveforms along the Datong-Qinhuangdao railroad in Northern China recorded in the suburban Huairou district of Beijing on March 8, 2003. It is illustrated that vibrations induced by train, except traditional recognized noises and interfer- ence effects, could be used as a seismic source to detect crustal structures with its advantage of abundant frequency spectrum, repeatability and no additional harm to the environment. It will bring lights to the traditional exploration seismology with the further studies of signal processing and interpretation methods, and related models and new observing systems.

Analysis theory of spatial vibration of high-speed train and slab track system

The motor and trailer cars of a high-speed train were modeled as a multi-rigid body system with two suspensions. According to structural characteristic of a slab track, a new spatial vibration model of track segment element of the slab track was put forward. The spatial vibration equation set of the high-speed train and slab track system was then established on the basis of the principle of total potential energy with stationary value in elastic system dynamics and the rule of ＂set-in-right-position＂ for formulating system matrices. The equation set was solved by the Wilson-θ direct integration method. The contents mentioned above constitute the analysis theory of spatial vibration of high-speed train and slab track system. The theory was then verified by the high-speed running experiment carried out on the slab track in the Qinghuangdao-Shenyang passenger transport line. The results show that the calculated results agree well with the measured rcsults, such as the calculated lateral and vertical rail displacements are 0.82 mm and 0.9 mm and the measured ones 0.75 mm and 0.93 mm, respectively; the calculated lateral and vertical wheel-rail forces are 8.9 kN and 102.3 kN and the measured ones 8.6 kN and 80.2 kN, respectively. The interpolation method, that is, the lateral finite strip and slab segment element, for slab deformation proposed is of simplification and applicability compared with the traditional plate element method. All of these demonstrate the reliability of the theory proposed.

Prediction of vibrations from underground trains on Beijing metro line 15

The impact of vibrations due to underground trains on Beijing metro line 15 on sensitive equipment in the Institute of Microelectronics of Tsinghua University was discussed to propose a viable solution to mitigate the vibrations.Using the state-of-the-art three-dimensional coupled periodic finite element-boundary element(FE-BE) method,the dynamic track-tunnel-soil interaction model for metro line 15 was used to predict vibrations in the free field at a train speed of 80 km/h.Three types of tracks(direct fixation fasteners,floating slab track and floating ladder track) on the Beijing metro network were considered in the model. For each track,the acceleration response in the free field was obtained.The numerical results show that the influence of vibrations from underground trains on sensitive equipment depends on the track types.At frequencies above 10 Hz,the floating slab track with a natural frequency of 7 Hz can be effective to attenuate the vibrations.

Pendulum systems for harvesting vibration energy from railroad tracks and sleepers during the passage of a high-speed train: A feasibility evaluation

We evaluate the feasibility of recovering energy from the vibrations of track and sleepers,during passage of a high-speed train,by means of a pendulum harvester.A simple mathematical model of the parametric pendulum is employed to obtain numerical predictions,while measured data of vibration tests during the passage of a Thalys high-speed train are considered as input forcing.Since a sustained rotation is the most energetic motion of a pendulum,the possibility of achieving such state is evaluated,taking into account the influence of initial conditions,damping and other factors.Numerical simulations show that rotating pendulum harvesters with sufficiently low viscous damping could be able to generate a usable average power on the order of 5–6 W per unit.Considering a modular arrangement of devices,such energy is enough to feed variety of rail-side equipment,as wireless sensors or warning light systems.However,a suitable choice of initial conditions could be a difficult task,leading to the need of a control action.

Effect of cross-wind on spatial vibration responses of train and track system

By taking cross-wind forces acting on trains into consideration, a dynamic analysis method of the cross-wind and high-speed train and slab track system was proposed on the basis of the analysis theory of spatial vibration of high-speed train and slab track system. The corresponding computer program was written by FORTRAN language. The dynamic responses of the high-speed train and slab track under cross-wind action were calculated. Meanwhile, the effects of the cross-wind on the dynamic responses of the system were also analyzed. The results show that the cross-wind has a significant influence on the lateral and vertical displacement responses of the car body, load reduction factor and overturning factor. For example, the maximum lateral displacement responses of the car body of the first trailer with and without cross-wind forces are 32.10 and 1.60 mm, respectively. The maximum vertical displacement responses of the car body of the first trailer with and without cross-wind forces are 6.60 and 3.29 mm, respectively. The maximum wheel load reduction factors of the first trailer with and without cross-wind forces are 0.43 and 0.22, respectively. The maximum overturning factors of the first trailer with and without cross-wind forces are 0.28 and 0.08, respectively. The cross-wind affects the derailment factor and lateral Sperling factor of the moving train to a certain extent. However, the lateral and vertical displacement responses of rails with the crnss-wind are almost the same as those without the cross-wind. The method presented and the corresponding computer program can be used to calculate the interaction between trains and track in cross-wind.

Vibration and acoustic radiation of bogie area under random excitation in high-speed trains

Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. Firstly, combined with line tests, a vehicle body with a length of 7 m was used as the research object. By comparing the results of experiment and simulation, the accuracy of the finite element model was verified. Secondly, the power spectral density curves at typical measuring points in bogie area were obtained by processing and calculating the line test data, which was measured when the vehicle ran at high speeds, and the standard vibration spectrum of the bogie area was obtained by the extreme envelope method. Furthermore, the random vibration test and simulation prediction analysis of the real vehicle structure were carried out to further verify the accuracy of the noise and vibration prediction model. Finally, according to the vibration and acoustic radiation theory, the indirect boundary element method was adopted to predict the acoustic response of the real vehicle. The analysis shows that the simulated power spectral density curves of acceleration and sound pressure level are highly consistent with the experimental ones, and the error between the simulated prediction and the experimental result is within the allowable range of 3 dB.

Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train

This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.

Coupling vibration analysis of high-speed maglev train-viaduct systems with control loop failure

The risk of failure of the control loop can occur when a high-speed maglev train runs on viaduct.Meanwhile,the failure of the levitation magnets which balances the gravity of the maglev train could cause the train collision with track.To study the dynamic response of the train and the viaduct when the levitation magnet control loop failure occurs,a high-speed maglev train-viaduct coupling model,which includes a maglev controller fitted by measured force-gap data and considers the actual structure of train and viaduct,is established.Then the accuracy and effectiveness of the established approach are validated by comparing the computed dynamic responses and frequencies with the measurement results.After that,the dynamic responses of maglev train and viaduct are discussed under normal operation and control loop failures,and the most disadvantageous combination of control loop failures is obtained.The results show that when a single control loop fails,it only has a great influence on the failed electromagnet,and the maglev response of adjacent electromagnets has no obvious change and no collision occurs.But there is a risk of rail collisions when the dual control loop fails.

Vibration and sound radiation of a rotating train wheel subject to a vertical harmonic wheel–rail force

The rapid development of high-speed railway networks requires advanced methods for analysing vibration and sound radiation characteristics of a fast rotating train wheel subject to a vertical harmonic wheel-rail force. In order to consider the rotation of the wheel and at the same time increase the computational efficiency, a procedure is adapted in this paper taking advantage of the axial symmetry of the wheel. In this procedure, a recently developed 2.5D finite element method, which can consider wheel rotation but only requires a 2D mesh over a cross section containing the wheel axis, is used to calculate the vibration response of the wheel. Then, the vibration response of the wheel is taken as acoustic boundary condition and the 2.5D acoustic boundary element method, which only requires a 1D mesh over the boundary of the above cross section, is utilised to calculate the sound radiation of the wheel. These 2.5D methods and relevant programs are validated by comparing results from this procedure with those from conventional 3D analyses using commercial software. The comparison also demonstrates that these 2.5D methods have a much higher computational efficiency. Using the 2.5D methods, we study the wheel rotation speed influences on the factors including the vertical receptance of the wheel at wheel-rail contact point, sound pressure level at a pre-defined standard measurement point, radiated sound power level, directivity of the radia- tion, and contribution of each part of the wheel. It can be concluded that the wheel rotation speed splits most peaks of the vertical receptance at the wheel-rail contact point, sound pressure levels at the field, and the sound power level of the wheel into two peaks. The directivity and power contribution of the wheel are also significantly changed by the wheel rotation speed. Therefore, the rotation of a train wheel should be taken into account when calculating its vibration and sound radiation.

Frost heave analysis of ballasted track above box culvert and its influence on train vibration

The uneven frost heave of frost-susceptible subgrade soil causes track irregularity,which highly enhances train vibration and affects the comfort and safety of railway transportation.This paper presents a coupled thermo-hydro-mechanical(THM)analysis for the freezing behavior of railway located above a box culvert.The vertical acceleration of the vehicle,an indicator of riding comfort,is predicted through a vehicle dynamic model.The results reveal that the existence of a box culvert changes the subgrade thermal pattern,leading to a deeper frost penetration depth.The frost heave amount above the box culvert is larger than the adjacent section,resulting in uneven track structure upheave and track irregularity.This frostinduced track irregularity highly affects train vibration.

Effects of vibration in desert area caused by moving trains

The ballast layer, filled with fine particles like blown sand, is one of the important problems of ballasted railway tracks in desert areas. Blown sand, as a contaminator of ballast layer, increases track stiffness and may cause serious damage to sleepers, pads, rails, and vehicles. In this paper, the effects of increasing track stiffness due to windy sands in the ballast layer and the train induced vibrations due to this phenomenon were studied. Based on field studies in a desert area in Iran, a two-dimensional finite/infinite element model for a railway track with plane strain condition was analyzed using the software ABAQUS, and the track vibrations were examined by changing the values of stiffness of ballast layer. Vibrations caused by the load of train at different distances from the cross-section of track were inves- tigated, and the values of vertical vibration displacement, velocity, and acceleration were calculated. Results show that acceleration values of vertical vibration increase with the increasing of ballast layer stiffness caused by the filling of sand, while the vertical vibration velocity of track and the induced ground displacement decrease. The farther the distance from the source of vibration, the less the displacement, velocity, and acceleration. In addition, the methods for reducing train-induced vibrations were introduced.

Prediction and mitigation analysis of ground vibration caused by running high-speed trains on rigid-frame viaducts

In this study a 3D numerical analysis approach is developed to predict the ground vibration around rigid-frame viaducts induced by running high-speed trains. The train-bridge-ground interaction system is divided into two subsystems： the train-bridge interaction and the soil-structure interaction. First, the analytical program to simulate bridge vibration with consideration of train-bridge interaction is developed to obtain the vibration reaction forces at the pier bottoms. The high- speed train is described by a multi-DOFs vibration system and the rigid-frame viaduct is modeled with 3D beam elements. Second, applying these vibration reaction forces as input external excitations, the ground vibration is simulated by using a general-purpose program that includes soil-structure interaction effects. The validity of the analytical procedure is confirmed by comparing analytical and experimental results. The characteristics of high-speed train-induced vibrations, including the location of predominant vibration, are clarified. Based on this information a proposed vibration countermeasure using steel strut and new barrier is found effective in reducing train-induced vibrations and it satisfies environmental vibration requirements. The vibration screening efficiency is evaluated by reduction VAL based on 1/3 octave band spectral analysis.