Dynamic studies of railtrack sleepers in a track structure system

This paper discusses the dynamic response of a typical prestressed concrete railtrack sleeper due to wheel-track interaction dynamics, involving wheel and rail imperfections, under various parametric conditions. The interaction dynamics of the vehicle and track is first carried out in the time domain using MSC/NASTRAN. Using the resulting load time histories on an isolated sleeper, a detailed finite element model of the sleeper is used to analyze its dynamic behaviour. The dynamic amplification factors for deflection, ballast pressure and bending moments have been evaluated at the critical section (rail-seat and centre) for various exciting frequencies under different vehicle-track parametric conditions. The results provide a basis for improved and rational design of the sleeper.     

Application of MetaRail railway noise measurement methodology: comparison of three track systems

Within the fourth RTD Framework Programme, the European Union has supported a research project dealing with the improvement of railway noise (emission) measurement methodologies. This project was called MetaRail and proposed a number of procedures and methods to decrease systematic measurement errors and to increase reproducibility. In 1999 the Austrian Federal Railways installed 1000 m of test track to explore the long-term behaviour of three different ballast track systems. This test included track stability, rail forces and ballast forces, as well as vibration transmission and noise emission. The noise study was carried out using the experience and methods developed within MetaRail. This includes rail roughness measurements as well as measurements of vertical railhead, sleeper and ballast vibration in parallel with the noise emission measurement with a single microphone at a distance of 7.5 m from the track. Using a test train with block- and disc-braked vehicles helped to control operational conditions and indicated the influence of different wheel roughness.It has been shown that the parallel recording of several vibration signals together with the noise signal makes it possible to evaluate the contributions of car body, sleeper, track and wheel sources to the overall noise emission. It must be stressed that this method is not focused as is a microphone-array. However, this methodology is far easier to apply and thus cheaper. Within this study, noise emission was allocated to the different elements to answer questions such as whether the sleeper eigenfrequency is transmitted into the rail.     

Symplectic analysis of vertical random vibration for coupled vehicle–track systems

A computational model for random vibration analysis of vehicle–track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli–Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle–track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.     

Ground vibrations from heavy freight trains

Ground vibration from heavy freight trains on good quality welded track are found to have only a weak dependence on train speed above 30 km/h. At the site on which these tests were carried out a critical speed was found at which the vibration reached a peak. The frequencies of vibration produced appear to be functions of track and vehicle dimensions and the critical speed occurs at the coincidence of sleeper passage frequency and the total vehicle on track resonance frequency.     

A rational fraction polynomials model to study vertical dynamic wheel–rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel–rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel–rail contact passing over a welding defect at different speeds.     

COUPLED WAVES ON A PERIODICALLY SUPPORTED TIMOSHENKO BEAM

A mathematical model is presented for the propagation of structural waves on an infinitely long, periodically supported Timoshenko beam. The wave types that can exist on the beam are bending waves with displacements in the horizontal and vertical directions, compressional waves and torsional waves. These waves are affected by the periodic supports in two ways: their dispersion relation spectra show passing and stopping bands, and coupling of the different wave types tends to occur. The model in this paper could represent a railway track where the beam represents the rail and an appropriately chosen support type represents the pad/sleeper/ballast system of a railway track. Hamilton's principle is used to calculate the Green function matrix of the free Timoshenko beam without supports. The supports are incorporated into the model by combining the Green function matrix with the superposition principle. Bloch's theorem is applied to describe the periodicity of the supports. This leads to polynomials with several solutions for the Bloch wave number. These solutions are obtained numerically for different combinations of wave types. Two support types are examined in detail: mass supports and spring supports. More complex support types, such as mass/spring systems, can be incorporated easily into the model.     

Symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track

Based on the pseudo-excitation method (PEM), symplectic mathematical scheme and Schur decomposition, the random responses of coupled vehicle-track systems are analyzed. The vehicle is modeled as a spring-mass-damper system and the track is regarded as an infinitely long substructural chain consisting of three layers, i.e. the rails, sleepers and ballast. The vehicle and track are coupled via linear springs and the “moving-vehicle model” is adopted. The latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero-mean valued stationary Gaussian random process. The problem is then solved efficiently as follows. Initially, PEM is used to transform the rail random excitations into deterministic harmonic excitations. The symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients. In turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the Schur decomposition scheme. Finally, the frequency-dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo-excitations. The proposed method is subsequently justified by comparison with a Monte-Carlo simulation; the fixed-vehicle model and the moving-vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed.     

On the railway track dynamics with rail vibration absorber for noise reduction

A promising means to increase the decay rate of vibration along the rail is using a rail absorber for noise reduction. Compound track models with the tuned rail absorber are developed for investigation of the performance of the absorber on vibration reduction. Through analysis of the track dynamics with the rail absorber some guidelines are given on selection of the types and parameters for the rail absorber. It is found that a large active mass used in the absorber is beneficial to increase the decay rate of rail vibration. The effectiveness of the piecewise continuous absorber is moderate compared with the discrete absorber installed in the middle of sleeper span or at a sleeper. The most effective installation position for the discrete absorber is in the middle of sleeper span. Over high or over low loss factor of the damping material used in the absorber may degrade the performance on vibration reduction.     

A double tuned rail damper—increased damping at the two first pinned-pinned frequencies

Railway-induced vibrations are a growing matter of environmental concern. The rapid development of transportation, the increase of vehicle speeds and vehicle weights have resulted in higher vibration levels. In the meantime vibrations that were tolerated in the past are now considered to be a nuisance. Numerous solutions have been proposed to remedy these problems. The majority only acts on a specific part of the dynamic behaviour of the track. This paper presents a possible solution to reduce the noise generated by the ‘pinned-pinned’ frequencies. Pinned-pinned frequencies correspond with standing waves whose nodes are positioned exactly at the sleeper supports. The two first pinned-pinned frequencies are situated approximately at 950 and 2200 Hz (UIC60-rail and sleeper spacing of 0.60 m). To attenuate these vibrations, the Department of MEMC at the VUB has developed a dynamic vibration absorber called the Double Tuned Rail Damper (DTRD). The DTRD is mounted between two sleepers on the rail and is powered by the motion of the rail. The DTRD consists of two major parts: a steel plate which is connected to the rail with an interface of an elastic layer, and a rubber mass. The two first resonance frequencies of the steel plate coincide with the targeted pinned-pinned frequencies of the rail. The rubber mass acts as a motion controller and energy absorber. Measurements at a test track of the French railway company (SNCF) have shown considerable attenuation of the envisaged pinned-pinned frequencies. The attenuation rate surpasses 5 dB/m at certain frequency bands.     

The influence of track modelling options on the simulation of rail vehicle dynamics

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.     

Determining the response of infinite, one-dimensional, non-uniform periodic structures by substructuring using waveshape coordinates

A method is presented for determining the wavenumbers, waveshapes and point receptances for an infinite, one-dimensional, non-uniform periodic structure with distributed periodic attachments or supports. The approach is based on a general theory of harmonic wave propagation in one-dimensional periodic systems. Ill-conditioning was previously reported as an impediment to applying the theory to problems of practical importance. In this paper ill-conditioning problems are overcome and a method of substructuring using waveshape coordinates is presented that dramatically improves computational efficiency. The accuracy and generality of the new method are tested by comparing computed and measured receptances for a typical TGV railway track with UIC60 rail, rail pad, ballast and concrete sleepers. The computed results are found to correlate well with measured data.     

A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements

This paper presents comparisons between a theoretical ground vibration model and measured data at three sites. The model, which is briefly outlined here, encompasses both the quasi-static and dynamic mechanisms of excitation. The vertical dynamics of a number of vehicles travelling at a constant speed on an infinite track are coupled to a semi-analytical model for a three-dimensional layered ground. This model is also used to demonstrate the roles of the two components of vibration at different frequencies and for train speeds below and above the lowest ground wave speed. It is found that, in most practical cases, the dynamic component gives rise to the higher level of vibration.     

Noise control for rapid transit cars on elevated structures

Noise control treatments for the propulsion motor noise of rapid transit cars on concrete elevated structures and the noise reduction from barrier walls were investigated by using acoustical scale models and supplemented by field measurements of noise from trains operated by the Port Authority Transportation Corporation (PATCO) in New Jersey. The results show that vehicle skirts and undercar sound absorption can provide substantial cost-effective reductions in propulsion noise at the wayside of transit systems with concrete elevated guideways. The acoustical scale model noise reductions applied to PATCO vehicles on concrete elevated structures show reductions in the A-weighted noise levels of 5 dB for undercar sound absorption, 5 dB for vehicle skirts, and 10 dB for combined undercar absorption and vehicle skirts. Acoustical scale model results for sound barrier walls lined with absorptive treatment showed reductions from 7 dB to 12 dB of noise from vehicles in the far track, depending on the height of the wall, and reductions from 12 dB to 20 dB of noise from vehicles on the near track. Transit vehicles at high speeds where propulsion system noise dominates are 7 dB(A) noisier at 50 ft on concrete elevated structures than on at-grade on tie and ballast. Of this amount, 3 dB is due to loss of ground effect, and 4 dB is due to the absence of undercar absorption provided by ballast.     

Fully three-dimensional analysis of high-speed train-track-soil-structure dynamic interaction

In this paper, a general and fully three dimensional multi-body-finite element-boundary element model, formulated in the time domain to predict vibrations due to train passage at the vehicle, the track and the free field, is presented. The vehicle is modelled as a multi-body system and, therefore, the quasi-static and the dynamic excitation mechanisms due to train passage can be considered. The track is modelled using finite elements. The soil is considered as a homogeneous half-space by the boundary element method. This methodology could be used to take into account local soil discontinuities, underground constructions such as underpasses, and coupling with nearby structures that break the uniformity of the geometry along the track line. The nonlinear behaviour of the structures could be also considered. In the present paper, in order to test the model, vibrations induced by high-speed train passage are evaluated for a ballasted track. The quasi-static and dynamic load components are studied and the influence of the suspended mass on the vertical loads is analyzed. The numerical model is validated by comparison with experimental records from two HST lines. Finally, the dynamic behaviour of a transition zone between a ballast track and a slab track is analyzed and the obtained results from the proposed model are compared with those obtained from a model with invariant geometry with respect to the track direction.     

The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks

The dynamic response of the railway track is strongly influenced by the underlying soil. For a soft soil and very high train speeds or for a very soft soil and regular train speeds, the train speed can be close to the speed of elastic waves in the soil. This paper presents a detailed study of the so-called “moving-load effect”, i.e. an amplification of the dynamic response due to the load movement, for the tracks on soft soil. The analysis is carried out by evaluating the related integrals in the wavenumber domain. The influence of the load speed is quantified for a large set of parameters, showing that the effect on the soil vibration is reduced with increase of the frequency, track width and inverse wave velocity. Therefore, the moving-load effect associated with vibratory train loads is negligible whereas the amplification associated with the moving dead weight of the train can be significant. The strong moving-load effect on a perfectly homogeneous soil, however, can be strongly diminished by a layered or randomly varying soil situation. This theoretical result is affirmed by measurements at a test site in Germany where the trains run on a very soft soil at a near-critical speed. The results for soft soils are compared with experimental and theoretical results for a stiff soil. It is found that the influence of the stiffness of the soil is much stronger than the moving-load effect. This holds for the soil vibration as well as for the track vibration which both show a minor dependence on the load speed but a considerable dependence on the soil stiffness in theory and experiment.Railway tracks can include soft isolation elements such as rail pads, sleeper shoes and ballast mats. For these types of isolation elements and normal soil conditions, the influence of the load speed is usually negligible. There is only one isolation measure for which the moving load may be effective: a track which is constructed as a heavy mass-spring system. The resonance of this track system is shifted to lower frequencies and amplitudes for increasing train speed. A critical train speed can be reached if the mass-spring system has a marginal bending stiffness along the track.     

非圆化磨耗激励下高速列车转向架区域噪声边频带产生机理及影响

该文通过对车辆噪声和车轮非圆化磨耗开展跟踪测试和分析,发现存在车轮非圆化磨耗的列车在运行过程中,其转向架区域噪声窄带频谱上会出现了以非圆化磨耗激励频率为中心,以过轨枕频率为间隔等间距分布的噪声峰值(即噪声边频带).这使得车轮非圆化磨耗不仅会影响其激励频率处的列车轨道结构的振动和噪声,还会对其他频段的噪声产生重要影响.为...     

Reducing slab track vibration into bridge using elastic materials in high speed railway

In this paper, the problem of vibration transmission from slab track structures into bridge is studied by theoretical analysis. A vehicle-track-bridge coupling system dynamics model is established based on a multibody dynamics theory and a finite element method. The system model consists of vehicle model, track-bridge model and wheel/rail interaction model. The vehicle model is established based on the multibody dynamics theory, and the tack-bridge model is established by the finite element method. The vehicle model and track-bridge model are coupled through wheel/rail interaction model, and the track irregularities are included. The system dynamic responses are calculated, and the effectiveness of elastic materials in vibration reducing is discussed. The results demonstrate that elastic materials like slab mat layer inserted between slab track and bridge can reduce vibration transmitted from track into the bridge. Some suggestions for the design and application of slab mat are provided in the end of the paper.     

Experimental study of granular compaction dynamics at different scales: grain mobility, hexagonal domains, and packing fraction

We present an original experimental study of the compaction dynamics for two-dimensional granular systems. Compaction dynamics is measured at three different scales: the macroscopic scale through the normalized packing fraction rho, the mesoscopic scale through the normalized fraction phi of hexagonal domains in the system, and the microscopic scale through the grain mobility mu. Moreover, the hexagonal domains are found to obey a growth process dominated by the displacement of domain boundaries. A global picture of compaction dynamics relevant at each scale is proposed.     

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.     

ANALYSES OF DYNAMIC RESPONSE OF VEHICLE AND TRACK COUPLING SYSTEM WITH RANDOM IRREGULARITY OF TRACK VERTICAL PROFILE

A dynamic computational model for the vehicle and track coupling system is developed by means of finite element method in this paper. In numerical implementation, the vehicle and track coupling system is divided into two parts; lower structure and upper structure. The vehicle as the upper structure in the coupling system is a whole locomotive or rolling stock with two layers of spring and damping system in which vertical and rolling motion for vehicle and bogie are involved. The lower structure in the coupling system is a railway track where rails are considered as beams with finite length rested on a double layer continuous elastic foundation. The two parts are solved independently with an iterative scheme. Coupling the vehicle system and railway track is realized through interaction forces between the wheels and the rail, where the irregularity of the track vertical profile considered as stationary ergodic Gaussian random processes and simulated by trigonometry series is included. The amplitudes of vibrations, their velocities and the accelerations generated in the vehicle and rail and the interaction forces between the vehicle and the rail due to the random irregularity of the track vertical profile and different line grades and train speeds have been analyzed numerically by this model. Analyses of system responses are performed in time and frequency domains.