Search

The environmental impacts of noise and vibration are becoming increasingly important in the assessment of new and upgraded railway routes. Vibration from railways propagates through the ground to nearby buildings where it may cause annoyance as feelable vibration or as re-radiated noise. To tackle the adverse effects of ground-borne noise a range of possible interventions are available, including softer rail pads, under-sleeper pads and under-ballast mats. The installation costs of such interventions are generally higher for the higher-performing track types. Additionally, there are potential effects on track maintenance costs which may be positive or negative, for example by reducing sleeper damage or increasing the need for ballast tamping. This study presents a socio-economic analysis of the effects of several interventions to reduce ground-borne noise. By selecting a whole route, the installation and whole-life costs are assessed using Network Rail’s Vehicle-Track Interaction Strategic Model (VTISM) and these are offset against benefits in terms of reduced social costs. Ground-borne noise is predicted at various distances from the alignment using the Modelling of Train Induced Vibration (MOTIV) model and the effect of track interventions is determined as insertion loss spectra. The re-radiated noise within a typical domestic building is then estimated using generic building transfer functions. Geographic Information System tools are used to estimate the population affected by ground-borne noise and their expected level of exposure. The methodology is illustrated using a case study route between Brighton and Portsmouth in the South of England.

Rectangular plates are important components in structures such as vehicles and bridges. The noise radiated by vibrating plates is mainly determined by three factors: the mean-square vibration, the radiation efficiency of the plates and the directivity of the sound. Although the first two factors have been widely investigated, much less attention has been paid to the directivity. The aim of this study is to investigate the directivity indices for rectangular plates subjected to either a single point force or multiple incoherent forces. Particular attention is given to plates with a large aspect ratio, referred to as plate strips. New definitions of directivity index are introduced that are more appropriate to such plate strips. The vibration of the plates is calculated from a modal superposition method based on approximate modal solutions of the plates with various boundary conditions. The Rayleigh integral method is used to obtain the sound pressure radiated from the vibrating plates, assuming that they are set in an ideal infinite baffle. Directivity indices of sound are firstly determined for plates with a small aspect ratio, and then for plate strips with a larger aspect ratio. Examples are given to illustrate the effects of the structural boundary conditions, and the effect of the baffle. For distributed incoherent excitation, as often found in practice, it is shown that the sound directivity pattern in the far field corresponding to the width direction varies insignificantly along the length of the strips; this is different from a single point force excitation. It is also found that the noise radiation from different concrete plates is approximately omnidirectional in the plane perpendicular to the longitudinal direction. Plates and plate strips are much less directional at high frequencies than the corresponding rigid piston. Nevertheless, the maximum value of directivity increases at high frequency as the number of modes in a one-third octave band increases. The dominant directions of sound radiation from plates are mainly controlled by the acoustical wavelength and vibrational wavelength, while the structural boundary conditions and the presence of the baffle have only a minor influence on them. Finally it is shown that, for the prediction of sound directivity of plate strips under distributed incoherent excitation, a two-dimensional vibro-acoustic model can be used in place of the three-dimensional one.

The operational speeds of passenger trains have been increasing and now often exceed 300 km/h. Higher speeds can lead to increased vibration and reduced ride comfort for railway passengers. This study investigates the combined effect of speed and track geometry on vibration discomfort in high-speed trains. Railway vehicle dynamic models with various levels of complexity are used, with the measured geometry of a section of a high-speed track as an input. The models have been calibrated with vibration measurements carried out in a train running over this section of the track and then applied to predict the vibration discomfort at increased speeds. To evaluate the vibration discomfort at speeds up to 400 km/h, information on track geometry should include wavelengths up to at least 150 m. Vertical irregularities have the greatest effect at all speeds but lateral irregularities are also important. Both the vertical and lateral irregularities of a high-speed track should be controlled at wavelengths of 50–100 m that excite rigid modes of the car body, corresponding to frequencies of typically 1–2 Hz. Additionally, vertical irregularities with wavelengths of 5–12 m that excite the fundamental flexible mode of the car body, typically around 10–15 Hz, should also be controlled. The effects of cant, the rates of change of cant, and the radius of vertical curves are also evaluated although they only have a small effect on vibration discomfort.

Conventional railway track is supported by a layer of crushed stones known as ballast. In recent years concrete slab tracks have been introduced which have been used widely in the construction of high-speed lines. However, a particular concern is that slab track is considered to be noisier than ballasted track. In order to investigate the differences in the noise radiation characteristics of ballasted and slab tracks, the TWINS model for rolling noise has been updated. Differences are included in the sound radiation of the rails and sleepers due to the presence of absorptive or reflective ground and the effect of the ballast vibration on the sound radiation of the sleepers is taken into account. The effects of the ballast absorption under the train on the sound propagation are also considered. To calculate the sound radiation from the slab itself, a waveguide finite element/boundary element method is used, which includes the supporting ground. The slab vibration is shown to be the dominant noise source only up to around 100 Hz, whereas it is negligible at higher frequencies. Results are presented for two ballasted tracks (one with stiff rail pads and the other with soft pads) and one slab track, and compared with measured data. Finally, the sound radiation from the various tracks are compared for equivalent situations. The results are found to depend on the assumptions made, particularly in relation to the track decay rates and roughness spectra; the ground conditions adjacent to the track also affect the sound pressure spectra below 1 kHz.

There is a great need to develop rail networks over long distances and within cities as more sustainable transport options. However, noise and vibration are seen as a negative environmental consequ...

More attention has been paid in recent years to the interior noise of railway vehicles. It has been observed that the interior noise can increase in some locations where vibration-isolation measures are used in the track structures. In order to assess the influence of vibration isolation measures on the noise levels inside railway vehicles, a field measurement campaign has been carried out. The vehicle interior noise has been measured when a train is running at different speeds over the same non-ballasted track section fitted with two types of rail fastener of different stiffnesses. Additional measurements of axlebox vibration, train floor vibration, exterior noise and rail vibration are used to investigate the influence of the fasteners further. The experimental results are compared with simulations performed using the TWINS model, considering the wheel/rail interaction, by focusing only on the relative differences between the two fastener systems. The axlebox vibration and rail vibration are predicted for a unit roughness input and the differences in rolling noise are also obtained. The predicted differences in axlebox vibration, rail vibration and rolling noise are in broad agreement with the measurement results. The results show that the fasteners with a lower stiffness cause a noisier interior environment. Around 125 Hz and in the frequency range 315–1000 Hz, the noise levels are higher for the more elastic fastener, with an average level difference of 3 dB in the latter frequency range. It appears from the shape of the level difference spectra that airborne noise has most influence between 100 and 400 Hz and structure-borne noise has more influence between 500 and 1000 Hz.

Made available in DSpace on 2019-10-06T15:18:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-01-01 There is an increasing desire to monitor the structural integrity of railway tracks and the supporting ballast and subgrade. Track vibration has been proposed as a potential energy source to power wireless sensors for this purpose. Vibration-based energy harvesting devices generally exploit resonance, and hence need to be tuned to a particular target frequency. Thus, to harvest energy from the vibrations of a passing train, the spectral content of the track vibration needs to be known. This paper describes a fundamental investigation into the factors that govern this spectral content. A simple model of the train and the track, together with data from five trains passing at four different sites are used in this investigation. It is shown that the deflection under an individual wheel effectively acts as a bandpass filter, restricting the acceleration spectrum of sleeper vibration to low frequencies. The train geometry has an important effect on which specific trainload frequency has the largest response amplitude. For the trains studied, it was found that the 7th trainload frequency had the highest amplitude in four out of the five cases. The physical reasons as to why this trainload frequency is the largest are discussed. Departamento de Engenharia Mecânica Universidade Estadual Paulista (UNESP) Department of Mechanical Energy and Management Engineering Univeristy of Calabria Institute of Sound and Vibration Research University of Southampton Departamento de Engenharia Mecânica Universidade Estadual Paulista (UNESP)

Due to local resonances, high vibration levels of the floor occur frequently in high-speed trains, which have a great negative impact on the ride comfort. A method is presented to control excessive local vibration of the internal floor of a high-speed electric multiple unit train by using multiple dynamic vibration absorbers (DVAs). The possible causes of the high vibration levels of the internal floor are investigated using operational and modal tests. To reduce the vibration, a model of the vehicle body with multiple DVAs is established based on the modal superposition method. The contribution of different modes at the dominant vibration peaks is assessed and targeted. It is found that a strong peak at around 12 Hz is dominated by a single mode, which can be attenuated by using a single DVA, which can be applied outside the car body, such as under-frame equipment. In the frequency region between 30 and 35 Hz several local modes contribute, and can be controlled by using multiple DVAs. Methods are studied to determine the optimal parameters for these DVAs, including location, natural frequency and mass. For a single DVA conventional fixed-point theory is used, whereas for multiple absorbers an optimization method is proposed. Finally, the effect of applying DVA solution is verified in the full vehicle model using frequency responses analysis. The results indicate that the proposed method can effectively reduce the vibration of targeted modes and improve the ride quality considerably in terms of the vertical motion.

Railway crossings are an important source of localized ground vibration. Models are required for identifying ways to tackle unacceptable levels of vibration from existing as well as future railway lines. Yet, the use of a prediction model that directly allows for the non-Hertzian wheel-rail contact dynamics and also includes three dimensional calculations of the ground response would be computationally expensive. In order to reduce the computational cost without affecting the accuracy of the predictions, a hybrid approach is proposed for the prediction of ground-borne vibration due to impacts at railway crossings. The approach combines the simulation of the vertical wheel-rail contact force in the time domain and the prediction of ground vibration levels in the far field using a linear wavenumber-frequency-domain approach. The proposed hybrid approach is used to investigate the influence of different vehicle speeds, crossing designs and wheel profiles on predicted ground vibration levels in the free field.

The dynamic properties of the rail fastening system affect the damping of the rail and the degree of coupling between the rail and the foundation. It is well known that the rate of decay of vibration along the rail is closely linked to the noise performance of the track. For this reason, the track decay rate (TDR) is used as an important measurable input quantity for models that predict railway rolling noise. This paper investigates whether the TDR can be estimated correctly from laboratory measured dynamic properties of rail fastening systems. The system studied in this work is a commercial two-stage baseplate system that is mounted on a slab track fitted with 60E1 rail. Four different types of rail pads were fitted during the track decay rates measurements. The TWINS model was used to predict the rolling noise using the measured and calculated track decay. The comparison has shown a good agreement between the measured and predicted TDR.

A number of different track forms are studied from one tramway system including tracks in ballast, on slab, and embedded rail in grass. Measurements have been carried out of rail roughness, wheel roughness and track decay rate, which are used as input data for the noise prediction model TWINS. The rail vibration and exterior noise of trams in operation have also been measured for comparison with the prediction model. The model is used to identify the relative contributions of noise radiated by the track and the wheels. The differences between different track forms are determined and the reasons for them are identified.

Complex-shaped stiffened panels are widely used nowadays in many structures such as railway vehicles, ships and offshore structures, in order to make them lighter and stronger. Therefore, it is essential to investigate vibration and radiation of the complex shaped panels to predict the vibro-acoustic performance of the large structures. In this paper, a coupled waveguide finite element and boundary element method, which can be applied where the cross-sectional properties of the panels are constant in one direction, is applied to predict the radiation efficiency of the extruded panel. The dependence of the radiation efficiency on two different types of excitation positions is investigated; a point force in the middle of the strip or on an interior stiffener. Finally, numerical results are validated through the comparison with experiments carried out with a 1.5 m length extruded panel.

[EN] An approach is presented for modelling the noise propagation beneath the train floor and this is applied to rolling noise sources. It is assumed that the sound incident on the train floor is made up of a direct and a reverberant component. A combination of two numerical modelling approaches is considered to deal with these: an equivalent source model, to represent the direct component, and statistical energy analysis (SEA) for the reverberant part. In the equivalent source model, the wheel is replaced by monopole and dipole sources, which represent its radial and axial radiation. The rail vertical vibration and the sleepers are replaced by arrays of monopole sources while the rail lateral vibration is replaced by an array of lateral dipoles. The sound power of the rolling noise is obtained by using the TWINS model. In the SEA model, the region beneath the train floor is divided into several volumes and the power input to these subsystems is assumed to be due to the first reflections from the train floor and the ground. The reverberant and direct sound have very similar contributions to the total sound power incident on the train floor although this depends on how the equipment is arranged beneath the train. The modelling approach is verified by comparing the predicted sound pressure levels with laboratory measurements and with field tests., This work has been funded by the China Scholarship Council and the RUN2Rail H2020/Shift2Rail project (Grant agreement No: 777564). The contents of this publication only reflect the authors' views and the Shift2Rail Joint Undertaking is not responsible for any use that may be made of the information contained in the paper. The authors would also like to thank Dr. Hongseok Jeong for his assistance in the laboratory measurements and Metro de Madrid for assistance in the field tests. All data published in this paper are openly available from the University of Southampton repository at 10.5258/SOTON/D1552.

In this paper, a wavenumber-domain boundary element (2.5D BE) approach is adopted to predict the transmission of noise from the wheels, the rails and the sleepers to the train external surfaces. In the 2.5D models, only the cross-section of the vehicle is created by using boundary elements, while the third direction is taken into account in terms of wavenumbers. After the sound pressure on the train cross-section is obtained, an inverse Fourier transform is applied to obtain the spatial distribution of the sound on the train surfaces. To validate this approach, the 2.5D boundary element method was used to predict the sound distribution on the train surfaces due to a point source below the vehicle, and due to the vibration of the track. The prediction of the sound distribution from the 2.5D method shows the sound pressure levels on the train floor are 20 dB higher than the pressure on the sides, and the pressure on the train roof caused by the sources below the vehicle is negligible. The 2.5D boundary element method was also used to predict the sound pressure spectrum on the train sides when the train was in running operation. Reasonable agreement was found with measurements.

Tramway noise can be significant even though the speeds are relatively low. The influence of track design on the rolling noise is studied through a systematic comparison of different tracks on a single network. These include a slab track with embedded sleeper blocks, a ballasted track and a track with embedded rails. Measurements have been taken of rail vibration and noise during tram passages at approximately 55 km/h; the rail and wheel roughness have also been measured. Comparisons are made in terms of track decay rate, rail vibration and pass-by noise. After normalising to the same roughness, the slab track is found to be the noisiest and the ballasted track the quietest. Theoretical models of the various track forms are also presented to give insight into the differences in acoustic performance. The models allow the relative contributions of the track and wheels to the pass-by noise to be identified. In addition the effect of rail dampers added to the slab track is assessed. These attenuate the noise at higher frequencies due to the increase in decay rate, but an increase in radiation is noted at 500 Hz and below, possibly linked to differences in effective roughness.

The prediction of the ground vibration transmitted from tunnels to neighbouring buildings is a vital step in the assessment of the ground-borne noise in buildings. In empirical models it is commonly assumed that the level of ground vibration reduces monotonically with the distance away from the tunnel alignment. In reality, a ‘shadow’ zone is observed above the tunnel. This is first illustrated using measurements made above an operational railway line. To understand and characterise this effect, a study has then been carried out using various simulation models. Using an analytical model for the response to a point force acting in a homogeneous full-space, it is shown that the response is principally in the form of shear waves which radiate to the side rather than compressional waves which radiate in the direction of the load. This leads to a ‘shadow’ zone forming above a certain frequency, even in the absence of a tunnel and the absence of a free ground surface. The ground surface is next introduced by considering the response of a half-space to a point force, using a semi-analytical model. This is shown to exhibit similar behaviour although with differences caused by the free ground surface. Finally, a numerical 2.5-dimensional finite element/boundary element model is used to determine the response of a half-space ground to a force acting at the bottom of a concrete tunnel. The extent of the shadow is defined as the width to the point of maximum response. This depends largely on the depth of the excitation force and the shear wave speed of the soil. Although similar features are found with or without the tunnel, the presence of the tunnel structure causes a reduction in the shadow width, and the level difference within the shadow region is slightly increased. A tunnel with a smaller diameter leads to an increase in the frequency at which a given shadow effect occurs, but the tunnel lining thickness has negligible influence. The existence of shadow effect should be taken into account when making predictions of ground vibration using empirical models.

In this study a hybrid finite element-statistical energy analysis (FE-SEA) method is used to investigate the structure-borne noise of a steel-concrete composite railway bridge. The rail is represented by an infinite Timoshenko beam connected to the sleepers which are regarded as finite Timoshenko beams supported in ballast. The fasteners and ballast are simplified as a series of springs with complex stiffness. This model allows the receptance of the track to be determined. The wheel-rail forces are computed in the frequency domain from the contact-filtered roughness and the receptances of the wheel, track, and contact. The forces transmitted to the bridge are determined by substituting the wheel-rail forces into the equation of motion for the track. This model could also be applied to a slab track mounted on a bridge. A hybrid FE-SEA method is introduced in which FE is used to model the concrete deck and SEA is used to model the steel girders. This enables the computation of the vibration and noise of the composite railway bridge. The proposed method is verified by comparing its predictions with field measurements. The structure-borne noise level of the bridge is found to increase with train speed v by approximately 20lg(v). It is shown that the adjacent spans in a multi-span bridge can be ignored in deriving the bridge-borne noise at receiver points in the middle of the main span, provided that the distance to the track centreline is less than 0.3 times the length of the main span.

Metal coil springs within primary suspensions in particular exhibit strong internal resonances, which can lead to high vibration amplitudes within the spring itself. A dynamic model of the metro vehicle-track coupled system is established, including the dynamic stiffness of the coil spring set. Two variants of the primary suspension are compared: one with the springset above the axlebox and the other with it offset on a radial arm. The effect of the primary suspension design on the random vibration response is analysed. From the results, it is shown that the internal resonances of the coil springs result in different vibration responses of the vehicle for the two cases. Although the dynamic stiffening effect of coil springs is expected to degrade the vibration isolation, for metro vehicles with a radial arm pivot bushing installation, this does not occur. Due to the rotation degree of freedom of the radial arm, the forces acting through the pivot bushing and coil spring set are out of phase, which decreases the bogie vibration at the spring resonances.

The noise produced during a train pass-by originates from several different sources such as propulsion noise, noise from auxiliary equipment, aerodynamic noise and rolling noise. The rolling noise is radiated by the wheels and the track and is excited by the wheel and rail unevenness, usually referred to as roughness. The current TSI Noise certification method, which must be satisfied by all new mainline trains in Europe, relies on the use of a reference track to quantify the noise from new vehicles. The reference track is defined by an upper limit of the rail roughness and a lower limit of the track decay rate (TDR). However, since neither the rail roughness nor the track radiation can be completely neglected, the result cannot be taken as representing only the vehicle noise and the measurement does not allow separate identification of the noise radiated by wheel and track. It is even likely that further reductions in the limit values for new rolling stock cannot be achieved on current tracks. There is therefore a need for a method to separate the noise into these two components reliably and cheaply. The purpose of the current study is to assess existing and new methods for rolling noise separation. Field tests have been carried out under controlled conditions, allowing the different methods to be compared. The TWINS model is used with measured vibration data to give reference estimates of the wheel and track noise components. Six different methods are then considered that can be used to estimate the track component. It is found that most of these methods can obtain the track component of noise with acceptable accuracy. However, apart from the TWINS model, the wheel noise component could only be estimated directly using three methods and un- fortunately these did not give satisfactory results in the current tests. QC 20180525 Roll2Rail

A numerical model is presented for the ground-borne vibration produced by trains running in tunnels. The model makes use of the assumption that the geometry and material properties are invariant in the axial direction. It is based on the so-called two-and-a-half dimensional (2.5D) coupled Finite Element and Boundary Element methodology, in which a two-dimensional cross-section is discretised into finite elements and boundary elements and the third dimension is represented by a Fourier transform over wavenumbers. The model is applied to a particular case of a metro line built with a cast-iron tunnel lining. An equivalent continuous model of the tunnel is developed to allow it to be readily implemented in the 2.5D framework. The tunnel structure and the track are modelled using solid and beam finite elements while the ground is modelled using boundary elements. The 2.5D track-tunnel-ground model is coupled with a train consisting of several vehicles, which are represented by multi-body models. The response caused by the passage of a train is calculated as the sum of the dynamic component, excited by the combined rail and wheel roughness, and the quasi-static component, induced by the constant moving axle loads. Field measurements have been carried out to provide experimental validation of the model. These include measurements of the vibration of the rail, the tunnel invert and the tunnel wall. In addition, simultaneous measurements were made on the ground surface above the tunnel. Rail roughness and track characterisation measurements were also made. The prediction results are compared with measured vibration obtained during train passages, with good agreement.

The dynamic stiffness of rail fasteners has a significant effect on the noise radiated by the rails as well as the vibration transmitted to the underlying structures, such as bridges, tunnels or track at grade. This study investigates the load- and frequency-dependence of a WJ-2A fastener which is commonly used in urban rail transit systems in China. This is a two-stage fastener with a rail pad and a baseplate pad separated by a steel plate. Results are obtained using the indirect measurement method in the frequency range 30 to 1000 Hz. The dynamic stiffness of the individual components is investigated as well as that of the whole fastener system and the combined stiffness of the components is verified by comparison with the whole fastener system. A numerical model of the test rig is used to provide understanding of various artefacts that are observed in the measurements and corrections are proposed to minimise their effects on the measured results. These allow for the differences between the response at the measurement positions and at the ideal positions at the interfaces between the fastener system and the rig. The stiffness magnitude of the rail pad, baseplate pad, and whole fastener system increases strongly with increasing static preload and increases weakly with increasing frequency; it is important to take these effects into account in prediction models for noise and vibration. The damping loss factors are not strongly dependent on preload or frequency. To describe the frequency-dependence, a fractional derivative Kelvin-Voigt (FDKV) model is introduced and is fitted to the dynamic stiffness with the help of a genetic algorithm method. The dynamic stiffness of the whole fastener system is influenced by both the rail pad and the lower baseplate pad. It is important to take account of both of them, as well as the internal resonance of the baseplate assembly which appears at around 1 kHz.

Concrete viaducts are an important part of urban rail transit systems but they produce considerable noise, thereby affecting the communities living nearby. The vibration generated at the wheel–rail interface is transmitted along the rail and also onto the bridge; hence, noise is radiated from both the rail and the bridge. To facilitate noise prediction, it is desirable to develop a model that takes into account the generation and transmission of vibration in the train–track–bridge system. The vibration and the associated noise of the track–bridge system are computed with a unified vibroacoustic model using a wavenumber domain finite element and boundary element method. An important aspect to note is the frequency-dependent stiffness of a typical rail fastener utilized on bridges due to the resonance of the baseplate between the two rubber pads. In this study, to allow for this effect, a multilayer fastener model is proposed. The proposed procedure is applied to a viaduct with a U-shaped section and compared with field measurements during the passage of trains. The elastic modulus and damping of the rubber pads and the equivalent loss factor of the rail are chosen by fitting the calculated track decay rates to those estimated from the measured rail accelerations under train passages. The wheel–rail combined roughness is also derived from the measured rail vibration. A comparison is then made between the simulated and measured bridge vibration to verify the proposed method as well as the parameters used in the track–bridge system. The predicted noise levels are also compared with the measured results. The effects of the fastener model, fastener stiffness, bridge damping, and interference between multiple wheels are then discussed. It has been found that the bridge noise has a non-negligible effect on the total A-weighted noise levels in the region beneath the bridge and up to 30 m away from the track.

This paper presents a methodology for studying ground vibration in which the railway track is modelled in the space-time domain using the finite element method (FEM) and, for faster computation, discretisation of the ground using either FEM or the boundary element method (BEM) is avoided by modelling it in the wavenumber-frequency domain. The railway track is coupled to the ground through a series of rectangular strips located at the surface of the ground; their vertical interaction is described by a frequency-dependent dynamic stiffness matrix whose elements are represented by discrete lumped parameter models. The effectiveness of this approach is assessed firstly through frequency domain analysis using as excitation a stationary harmonic load applied on the rail. The interaction forces at the ballast/ground interface are calculated using the FE track model in the space-time domain, transformed to the wavenumber domain, and used as input to the ground model for calculating vibration in the free field. Additionally, time domain simulations are also performed with the inclusion of nonlinear track parameters. Results are presented for the coupled track/ground model in terms of time histories and frequency spectra for the track vibration, interaction forces and free-field ground vibration. For the linear track model, the results from the mixed formulation are in excellent agreement with those from a semi-analytical model formulated in the wavenumber-frequency domain, particularly in the vicinity of the loading point. The accuracy of the mixed formulation away from the excitation point depends strongly on the inclusion of through-ground coupling in the lumped parameter model, which has been found to be necessary for both track dynamics and ground vibration predictions.

In a conventional railway track, the rails are laid on sleepers, usually made of concrete, which are supported by a layer of coarse stones known as ballast. This paper focuses on quantifying the influence that the ballast has on the noise produced by the vibration of the track, particularly on the rail and sleeper radiation ratios. A one-fifth scale model of a railway track has been used to conduct acoustic and vibration measurements. This includes reduced-scale ballast that has been produced with stone sizes in the correct proportions. Two different scaling factors (1:√5 and 1:5) have been adopted for the stone sizes in an attempt to reproduce approximately the acoustic properties of full-scale ballast. It is shown that, although a scale factor of 1:√5 gives a better scaling of the acoustic properties, the stones scaled at 1:5 also give acceptable results. The flow resistivity and porosity of this ballast sample have been measured. These have been used in a local reaction model based on the Johnson-Allard formulation to predict the ballast absorption, showing good agreement with measurements of the absorption coefficient. The effects of the presence of the ballast on the noise radiation from a reduced-scale steel rail and concrete sleeper have been investigated experimentally with the ballast located on a rigid foundation. Comparisons are made with the corresponding numerical predictions obtained by using the boundary element method, in which the ballast is represented by a surface impedance. Additionally the finite element method has been used in which the porous medium is considered as an equivalent fluid. From these results it is shown that the extended reaction model gives better agreement with the measurements. Finally, the effects of the ballast vibration on the sleeper radiation have also been investigated for a case of three sleepers embedded in ballast. The ballast vibration is shown to increase the sound radiation by between 1 and 4.5 dB for frequencies between 20 and 300 Hz at full scale whereas at higher frequencies the effect is negligible.

Recent work in rail vibration has investigated methods for estimating track support stiffness from trackside vibration. This vibration, induced by the passage of a train, is mainly due to the load applied by the wheels, and is known as quasi-static excitation. It is characterized by dominant peaks in the vibration spectrum that are an integer multiple of the ratio between the speed and length of a train carriage. In this paper the behaviour of the vertical rail deflection is investigated to determine the physical reasons why the vibration at certain frequencies is greater than at others. A simple model is used to determine the contribution of the train geometry and the track parameters to the shape of the rail deflection spectrum. The model is also validated with data from various trains and at various sites. It is found that the track properties influence the range of frequencies at which there is significant vibrational energy, but the specific frequencies where there is large vibration are mainly a function of the train geometry.

Beam stiffening technique has been widely used in engineering application to minimize the vibration of structures, to increase its loading capacity and to prevent the structure from buckling. However, study on the sound radiation from the beam stiffened plate is still lacking. This paper mainly presents the experimental setup to measure the radiation efficiency of three-beam and the five-beam stiffened plates. The treatment for the test plate is discussed. Reciprocity technique was employed to measure the sound power. In general, the measured results for the acoustic power show good agreement with those from the proposed mathematical model. Measured radiation efficiencies overestimate the simulation results of high frequencies due to error in the mobility measurement.

Environmental noise is an issue that has seen increased awareness in recent years. In this chapter, the various sources of noise and vibration are summarised and methods to control them are discussed. The main source of noise from the railway system is rolling noise from the wheel-rail contact. Models for this are described leading to an overview of potential methods to control it. In addition, impact noise due to wheel flats and rail joints and squeal noise in sharp curves are considered. At high speed, aerodynamic noise becomes dominant due to its higher speed dependence. All these sources of noise can be transmitted to the vehicle interior as well as radiated to the wayside; both structure-borne and airborne transmission paths need to be considered. Ground vibration is also produced, which can be experienced as feelable vibration and as low-frequency re-radiated noise. Methods to control ground-borne noise include resilient track forms; feelable vibration is more difficult to control, although it is important to minimise the vehicle unsprung mass. Finally, ride comfort and the influence of the vehicle suspension are discussed.

Ride comfort indices are used to evaluate the vibration of rail vehicles and to measure the discomfort of passengers. Among the various ride comfort indices, the Sperling index is widely used in China and other countries. However, there are several different methods for determining the Sperling index from dynamic simulations and performance measurements of rail vehicles, and the results obtained by different algorithms are inconsistent.It is therefore difficult to make an accurate evaluation with the different calculation results. In this paper, a comparison is made between algorithms based on time domain and frequency domain analysis and using the second and third powers of the acceleration.The different algorithms are then summarized into a unified equation, and the consistency of the results is analyzed by this equation. It is found that only the r.m.s-based algorithm in the time or frequency domain is stable when analysis is carried out over different sample times. The time-frequency consistency of the r.m.s-based algorithms is verified by Parseval’s theorem and using calculation results from time domain simulations.

As train speeds are increased, the issue of the critical speed must be faced, especially when tracks run across soft ground. This is the phenomenon describes the amplification of the track deflections due to coincidence of the train speed with the wavespeeds of the underlying ground. Modern high-speed lines are often constructed on ballastless track which has different dynamic behaviour to conventional ballasted track. Therefore, further research is needed to investigate the critical speed of ballastless track. In this paper, a dynamic analysis model comprising track, embankment and ground is presented based on the two-and-half-dimensional (2.5D) finite element method to predict the vibrations generated by train moving loads. The rails and track slab are modeled as Euler-Bernoulli beams resting on the embankment. The concrete base, embankment and ground are modeled by the 2.5D finite elements. The results show that the critical speed of ballastless track is higher than the Rayleigh wave velocity of the underlying soil and quite close to the Rayleigh wave velocity of the subgrade. The existence of the subgrade can highly improve the critical speed of the ballastless track even with a shallow subgrade of 1.25 m depth. The underlying soil stiffness is the conclusive factor in determining the track vibration amplitude. It is also found that the embankment plays an essential role in reducing the inhomogeneity of the lateral stress distribution and the amplitude of vertical stress in ballastless track.

The dynamic properties of a railway track are important for both the generation of rolling noise and the development of rail corrugation. A conventional track consists of long rails mounted periodically on transverse sleepers and supported in ballast. In order to improve the predictions of the noise and vibration of the track, a model of a discretely supported track is proposed based on the so-called 2.5 dimensional (2.5D) finite element approach, which is used to model an infinite free rail. This is coupled to a finite number of sleepers, by means of an array of springs representing each rail pad, using a receptance coupling method. The sleepers are represented by flexible beams, supported on an elastic foundation. Results are presented in terms of the point mobility and track decay rate and these are compared with the corresponding field measurements for two tracks, one with soft rail pads and one with stiff rail pads. Very good agreement is found between the predictions and the measurement results, especially for the track with soft rail pads. The flexible sleeper model is shown to give improved results compared with a rigid mass model, especially for the track with stiff rail pads.

With the development of non-ballasted track forms (often referred to as slab tracks) over the few last decades, it is important to understand their behaviour with respect to ground-borne vibration compared with the traditional ballasted tracks. This is important in deciding between the use of the two track forms. The present work aims to quantify the differences between slab tracks and ballasted tracks numerically by using the MOTIV model. This is a general and fully coupled three-dimensional model that works in the wavenumber-frequency domain. It can predict the vibration levels of the track and the ground due to the gravitational loading of a passing train and the wheel and rail unevenness. A comparative analysis between the two track types is presented in terms of ground vibration with emphasis given to the influence of the stiffness and inertial parameters of the two track forms. It is shown that, for the same fastener stiffness there are only small differences in ground vibration behaviour, with the mass of the track slab leading to reductions of 1–3 dB at frequencies above 16 Hz. However, if softer rail fasteners are used in the slab track, as is usual, this leads to further reductions above 63 Hz. The critical velocity on soft soil is also considered. Although there is little difference between the different tracks for a homogeneous ground, for grounds with a soft surface layer the critical velocity is increased by the slab bending stiffness. The maximum rail displacement is also smaller for a slab track than the equivalent ballasted track. The work described here has been supported by the EPSRC under the programme grant EP/M025276/1, ‘The science and analytical tools to design long life, low noise railway track systems (Track to the Future)’ and the MOTIV project (Modelling of Train Induced Vibration), grants EP/K005847/2 and EP/K006002/1. All data published in this article are openly available from the University of Southampton repository at https://doi.org/10.5258/SOTON/D1001. Scopus

Slab track is generally noisier than conventional ballasted track, so noise control measures that can be applied to a slab track are of great importance. Several noise control treatments have been studied under controlled conditions through experiments on a 1:5 scale model slab track with and without the presence of a train body. These treatments consist of absorptive rubber mats applied to the surface of the slab and a low noise barrier introduced close to the track. The noise reduction is evaluated experimentally by using a reciprocal method and compared with the results of numerical simulations. The insertion loss spectra of these treatments have been combined with predicted train pass-by spectra to determine the potential overall noise reductions. It has been found that the absorptive treatment alone has only a small effect on the radiated noise from the track. This is increased by the presence of the train body leading to a reduction of up to 2–3 dB at a standard receiver height of 1.2 m, which suggests that the absorptive layer controls reflections between the car body and the track. All the treatments considered have a greater effect on the noise radiated by the lateral vibration of the rail than on that from the vertical vibration. Their effectiveness mostly increases, by between roughly 0.5 and 1.5 dB, as the train speed is increased from 80 to 300 km/h. As expected, the noise barrier is more effective at lower receiver positions than at higher ones but its effectiveness is reduced by 1–2 dB by the presence of the train body. However, in combination with the absorptive treatment, its effectiveness increases when the train body is present. This shows the importance of including of the presence of the train body in evaluating the effects of acoustic treatments in the track.

A novel computational modelling approach for prediction of environmental vibration is introduced. The model is formulated in both moving and fixed frames of reference, with a mixed frame of reference formulation introduced to couple the two frames of reference. The resulting system is able to model a vehicle travelling on an infinite railway track, formulated in a moving frame of reference, interacting via the soil with a structure (i.e. building), formulated in a fixed frame of reference. The method utilizes a semi-analytical soil model with the structures modelled using three-dimensional finite elements. Two solution procedures of the full system are proposed: partial coupling, where some secondary effects from reflected waves propagating through soil are disregarded, and full coupling, where the vehicle–track–soil–structure is modelled as a fully coupled system. Both proposed solution procedures offer a one-step approach for solving the whole system in the frequency–spatial domain. The usage of the model is demonstrated in two example cases: one analysing a simple building structure near a railway track, using the partial coupling solution procedure, and another one analysing the behaviour of a vehicle model traversing over a rigid block embedded inside the soil, using the full coupling solution procedure. The introduced modelling approach offers a computationally efficient solution procedure, at the same time being applicable to a wide array of application cases.

Made available in DSpace on 2018-12-11T16:40:46Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-01-01 With the advent of wireless sensors, there has been an increasing amount of research in the area of energy harvesting, particularly from vibration, to power these devices. An interesting application is the possibility of harvesting energy from the track-side vibration due to a passing train, as this energy could be used to power remote sensors mounted on the track for strutural health monitoring, for example. This paper describes a fundamental study to determine how much energy could be harvested from a passing train. Using a time history of vertical vibration measured on a sleeper, the optimum mechanical parameters of a linear energy harvesting device are determined. Numerical and analytical investigations are both carried out. It is found that the optimum amount of energy harvested per unit mass is proportional to the product of the square of the input acceleration amplitude and the square of the input duration. For the specific case studied, it was found that the maximum energy that could be harvested per unit mass of the oscillator is about 0.25 J/kg at a frequency of about 17 Hz. The damping ratio for the optimum harvester was found to be about 0.0045, and the corresponding amplitude of the relative displacement of the mass is approximately 5 mm. Department of Mechanical Energy and Management Engineering University of Calabria Departamento de Engenharia Mecãnica Universidade Estadual Paulista (UNESP) Institute of Sound and Vibration Research University of Southampton Departamento de Engenharia Mecãnica Universidade Estadual Paulista (UNESP)

Tracks with rails embedded in a layer of rubber are commonly used for tramways. The vibration and sound radiation behaviour of these tracks differs from that of conventional railway tracks. This is studied here using coupled wavenumber finite element and boundary element models. A detailed analysis is carried out for an embedded rail with a narrow embedding material and comparisons are made with field measurements. The rail, embedding material and surrounding concrete are modelled with finite elements, whereas the support conditions due to the underlying ground are modelled with structural boundary elements coupled to the base of the track model. The sound radiation is calculated using a wavenumber acoustic boundary element model in which it is assumed that there is only one-way coupling with the structure. At low frequencies, vibration of the concrete slab also contributes to the noise radiation. Consequently, the radiated sound is increased compared with that produced by the rail alone at low frequencies but it is reduced above 300 Hz, where the rail and concrete vibrate out of phase with one another; at frequencies above 500 Hz the concrete has negligible effect. The track decay rate has a broad minimum between 500 and 1000 Hz; the noise radiation therefore has a peak in this important frequency region. However, the decay rate increases strongly above 1000 Hz due to the influence of the embedding material. The track considered has a grass in-fill between and outside the rails and allowing for the absorptive effect of the grass leads to a small reduction in the sound radiation. In addition, the attenuation effect of the fairings around the bogie region is estimated taking account of the absorptive effect of the grass surface. The embedded rail models are coupled with a model of a tram wheel and used to predict the rolling noise during the passage of a tram, showing good agreement with field measurements. Finally, various alternative embedded rail designs are compared, including different shapes of the embedding material and different rail profiles. Differences of up to 3 dB are found between the various designs.

Conventional railway tracks are laid in a layer of crushed stone known as ballast which contributes to the resilience of the track support. Beneath it is the subgrade which also has a considerable influence on the track support stiffness. Although quasi-static measurements of track stiffness are reasonably common, the dynamic stiffness at higher frequencies is required for noise and vibration modelling. Here, a distinction is made between the dynamic stiffness of the ballast layer itself and the dynamic support stiffness which includes the underlying ground. The dynamic transfer stiffness of a ballast layer is required for ground vibration and bridge noise predictions. Two different methods for measuring this are presented, one in the laboratory and the other in the field. The laboratory method is limited to a maximum frequency of about 600 Hz due to limitations of the test rig. The field measurement, which relies on identifying the wavespeed within the medium, gives results up to 2 kHz. These methods give broadly consistent results, with a stiffness per rail seat for a 300 mm thick ballast layer of approximately 300–500 MN/m, increasing in proportion to the square root of the preload, and a damping loss factor in the range 0.15–0.3. The corresponding Young's modulus is between 200 and 700 MPa, depending on the preload. The dynamic stiffness increases above about 300 Hz with a first peak due to standing wave effects occurring at about 700 Hz. The dynamic support stiffness beneath the sleeper, on the other hand, is required for rolling noise modelling. This has been measured using two methods: a direct method for frequencies 50–500 Hz and an indirect method based on a modal analysis of a sleeper embedded in the ballast. A clear shift in natural frequencies is seen which is associated with the support stiffness. This support stiffness is strongly frequency-dependent, with the value per rail seat increasing from about 100 to 200 MN/m at 100 Hz to 2000 MN/m at 1 kHz. The support damping corresponds to a loss factor of around 1 for frequencies above 200 Hz, or a damping coefficient of 100–200 kN/m per rail seat. This damping is due to the radiation of energy into the ground rather than internal losses in the ballast. It strongly affects the modal damping of the sleeper and thus its radiated noise. The dynamic support stiffness increases roughly in proportion to the cube root of the preload. Comparison with a finite element model indicates that the underlying ground is responsible for the support stiffness and damping at low frequencies. However, above about 500 Hz it is independent of the ground and is only affected by the ballast layer. The results from the finite element model imply behaviour similar to a viscous damper. The sleeper vibration obtained using either a viscous damping or a constant loss factor is similar.

Rolling noise from running trains is significantly influenced by the wheel–rail combined roughness and the dynamic properties of the track. To facilitate predictions of vibration and noise, it is desirable to be able to determine these parameters accurately from field measurements. In this study, an inverse method for the determination of these parameters is adopted and enhanced. A track model that is based on a wavenumber finite element model of the free rail coupled to discrete supports, which allows for the pinned–pinned mode and cross–sectional deformation of the rail, has been used. The rail vibration induced by hammer impacts and the vibration during train passages are simulated using this model, and these results are then applied to illustrate the accuracy of the direct and indirect methods for the estimation of track decay rate. These methods are compared in a case study for a ballasted track for which hammer impact and train pass–by measurements have been obtained. Other track parameters can also be extracted from the measured data by using the advanced track model. Thereafter, a more complete method is adopted to estimate the wheel–rail combined roughness from the measured rail vibration under train passages. A comparison is made among the estimated roughness levels obtained from this full method, an existing simplified method and the direct measurement method. It is found that the simplified method overestimates the roughness around the pinned–pinned resonance frequency, but gives a good estimation if the track decay rates of the loaded track are used.

Curve squeal is one of the most annoying types of noise caused by the railway system. It usually occurs when a train or tram is running around tight curves. Although this phenomenon has been studied for many years, the generation mechanism is still the subject of controversy and not fully understood. A negative slope in the friction curve under full sliding has been considered to be the main cause of curve squeal for a long time but more recently mode coupling has been demonstrated to be another possible explanation. Mode coupling relies on the inclusion of both the lateral and vertical dynamics at the contact and an exchange of energy occurs between the normal and the axial directions. The purpose of this paper is to assess the role of the mode-coupling and falling-friction mechanisms in curve squeal through the use of a simple approach based on practical parameter values representative of an actual situation. A tramway wheel is adopted to study the effect of the adhesion coefficient, the lateral contact position, the contact angle and the damping ratio. Cases corresponding to both inner and outer wheels in the curve are considered and it is shown that there are situations in which both wheels can squeal due to mode coupling. Additionally, a negative slope is introduced in the friction curve while keeping active the vertical dynamics in order to analyse both mechanisms together. It is shown that, in the presence of mode coupling, the squealing frequency can differ from the natural frequency of either of the coupled wheel modes. Moreover, a phase difference between wheel vibration in the vertical and lateral directions is observed as a characteristic of mode coupling. For both these features a qualitative comparison is shown with field measurements which show the same behaviour.

Two parametric studies have been conducted in order to examine the influence of a number of building and room parameters on the groundborne noise and vibration levels in a room. The studies have each utilised a three-dimensional finite element (FE) approach, validated with site measurements. It was found that changing the floor thickness had a limited effect on floor vibration, whereas changing the floor area was found to be more important, due to shifting the floor mode frequencies. Structural damping was shown to be important, and should therefore be specified carefully when modelling building vibration. The FE model of a typical domestic room demonstrated that there is significant variation in groundborne noise at different room positions due to the influence of acoustic modes. It is therefore recommended that the low frequency procedure detailed in ISO 16283-1 be adopted for specifying and measuring groundborne noise in such rooms. The parametric study showed that the room reverberation time, room size and presence of furniture each have a moderate effect on the sound pressure level. Whilst the installation of wall linings was predicted to provide only a marginal improvement in sound pressure level, this effect is dependent on the relative contributions of the wall, ceiling and floor surfaces. Results from the parametric studies are being used to inform semi-empirical prediction formulae for groundborne noise and vibration.

The speed of passing trains is conventionally estimated using Doppler speed guns, or optical sensors. However in many cases, these techniques are not applicable when the measured trains are not visible (for example in tunnels) or close access to the track is not possible. An alternative method to estimate train speed from ground vibration measurements is presented in this paper. The method takes advantage of the relation between vibration levels and the cyclic repetition of the excitation forces created by the wheels. A train mask, expressed in the wavelength domain, is derived from a simple rail deflection model induced by the train wheels. The vibration spectrum at very low frequency and the train mask are qualitatively compared to match the various peaks. Vibration and train speed measurements have been undertaken near St Denys station, Southampton. Very good agreements have been observed between the direct train speed measurements and the proposed estimation method.

When trains run on soft ground, large deflections of the track and vibration of the ground can occur when the train speed approaches the speed of Rayleigh waves in the ground. Modelling is helpful to understand and mitigate such critical velocity effects. Here, a three-dimensional time-domain model of a load moving on a track and ground has been developed with the finite element software ABAQUS. This allows nonlinear soil properties to be considered. In order to validate the approach, the vibration of the track and ground induced by a high speed train is compared with those from the site measurements carried out in the late 1990s at Ledsgård, Sweden. Due to the particularly soft soil at this site, it is necessary to adopt a nonlinear soil model due to the large deflections induced by the high-speed train. It is shown that using a linear model based on the small strain soil parameters leads to results which underestimate the displacements. Laboratory test data allow the nonlinear characteristics to be obtained. These have previously been used by various authors in an equivalent linear model. Here this approach is compared with a fully nonlinear model.

Rail dampers work by increasing the attenuation with distance of vibration transmitted along the rail, a quantity known as the track decay rate. Currently, there are no standardized procedures to measure their effectiveness in reducing rolling noise without the need for in-track installation and time-consuming tests. This paper describes and evaluates experimental procedures for assessing rail dampers. Instead of field measurements it is proposed to use laboratory measurements of vertical and lateral decay rates on a free rail equipped with dampers. These are combined with in-situ measurements on an undamped track. The decay rates of a damped track can be approximated by adding the results of the damped free rail to those of the undamped track.Three different methods are studied to measure the decay rates of damped free rails: (i) using a long rail, in the present work 32 m long, from frequency response functions measured at intervals along the rail; (ii) using a short rail, in the present work 6 m long, from the modal properties of the rail; and (iii) directly from the point and transfer frequency response functions at both ends of the short rail. The latter two are complementary: the modal method is more suited to low frequencies while the direct method is more suited to high frequencies. These methods are evaluated theoretically and by comparison with experimental results.Good agreement is found between the various methods, for vibration in both vertical and lateral directions, between 300 Hz and 5 kHz. In practice, the direct short-rail method is likely to be sufficient for most applications. The limitations of the methods are identified and corrections are proposed for the effect of near-field waves in the rail

The prediction of ground vibration from trains presents a number of difficulties. The ground is effectively an infinite medium, often with a layered structure and with properties that may vary greatly from one location to another. The vibration from a passing train forms a transient event, which limits the usefulness of steady-state frequency domain models. Moreover, there is often a need to consider vehicle/track interaction in more detail than is commonly used in frequency domain models, such as the 2.5D approach, while maintaining the computational efficiency of the latter. However, full time-domain approaches involve large computation times, particularly where three-dimensional ground models are required. Here, a hybrid modelling approach is introduced. The vehicle/track interaction is calculated in the time domain in order to be able t account directly for effects such as the discrete sleeper spacing. Forces acting on the ground are extracted from this first model and used in a second model to predict the ground response at arbitrary locations. In the present case the second model is a layered ground model operating in the frequency domain. Validation of the approach is provided by comparison with an existing frequency domain model. The hybrid model is then used to study the sleeper-passing effect, which is shown to be less significant than excitation due to track unevenness in all the cases considered.

Measurements of low-frequency vibration are increasingly being used to assess the condition and performance of railway tracks. Displacements used to characterise the track movement under train loads are commonly obtained from velocity or acceleration signals. Artefacts from signal processing, which lead to a shift in the datum associated with the at-rest position, as well as variability between successive wheels, mean that interpreting measurements is non-trivial. As a result, deflections are often interpreted by inspection rather than following an algorithmic or statistical process. This can limit the amount of data that can be usefully analysed in practice, militating against widespread or long-term use of track vibration measurements for condition or performance monitoring purposes. This paper shows how the cumulative distribution function of the track deflection can be used to identify the at-rest position and to interpret the typical range of track movement from displacement data. This process can be used to correct the shift in the at-rest position in velocity or acceleration data, to determine the proportion of upward and downward movement and to align data from multiple transducers to a common datum for visualising deflection as a function of distance along the track. The technique provides a means of characterising track displacement automatically, which can be used as a measure of system performance. This enables large volumes of track vibration data to be used for condition monitoring.

The high frequency dynamic behaviour of railway tracks, in both vertical and lateral directions, strongly affects the generation of rolling noise as well as other phenomena such as rail corrugation. An improved semi-analytical model of a beam on an elastic foundation is introduced that accounts for the coupling of the vertical and lateral vibration. The model includes the effects of cross-section asymmetry, shear deformation, rotational inertia and restrained warping. Consideration is given to the fact that the loads at the rail head, as well as those exerted by the railpads at the rail foot, may not act through the centroid of the section. The response is evaluated for a harmonic load and the solution is obtained in the wavenumber domain. Results are presented as dispersion curves for free and supported rails and are validated with the aid of a Finite Element (FE) and a waveguide finite element (WFE) model. Closed form expressions are derived for the forced response, and validated against the WFE model. Track mobilities and decay rates are presented to assess the potential implications for rolling noise and the influence of the various sources of vertical-lateral coupling. Comparison is also made with measured data. Overall, the model presented performs very well, especially for the lateral vibration, although it does not contain the high frequency cross-section deformation modes. The most significant effects on the response are shown to be the inclusion of torsion and foundation eccentricity, which mainly affect the lateral response. This work has been sponsored by Network Rail and the Engineering and Physical Sciences Research Council under the grant reference 1342762. All data published in this paper are openly available from the University of Southampton repository at: http://dx.doi.org/10.5258/SOTON/404573. Scopus

A model of the vibration behaviour of a discontinuous slab track installed on a viaduct is presented. It is represented by a three-layer Euler–Bernoulli beam model subjected to a harmonic load. Analytical equations are derived using the receptance method, and they are used to determine the vibration properties of the system. Comparisons are made between the vibration behaviour under various parameter conditions of the Chinese CRTS I slab track and a typical floating slab track installed on a viaduct. Attention is focused on the mobility, vibration isolation and track decay rates. The results show that, as expected, the floating slab track generates significantly lower viaduct vibrations than the CRTS I slab track. A slab track fitted with a relatively stiff rail pad and soft bearing layer is recommended for consideration during the engineering design phase; appropriate choices can lead to the optimization of the vibration isolation performance of a railway track on a viaduct, thus avoiding the creation of excessive rail vibrations. It is also shown that the average response of the viaduct gives a more representative assessment of the vibration isolation effect than if the average force transmitted to the viaduct is used. Moreover, in terms of insertion loss, these results are relatively insensitive to the choice of viaduct parameters.

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.

The Railway Rolling Noise Prediction Software (RRNPS) is a model for predicting the sound pressure levels (SPLs) during a train passage due to wheel/rail roughness, based on vibration dynamics, contact mechanics and sound radiation modules. Similar software has been developed previously, in particular the Track–Wheel Interaction Noise Software (TWINS) model, and some field validation has been done under European and Japanese conditions. In this article, the RRPNS is used to model a typical railway rolling noise situation in Australia and compared with detailed field experimental results for validation purposes. A series of field measurements were taken at a narrow track gauge testing site in Australia. Comparisons between simulations and measurements have shown that this software model gives reliable predictions in terms of overall A-weighted SPL and noise spectrum. In addition, a sensitivity analysis of the model was carried out to investigate the effect of speed, normal load, ballast vertical stiffness,...