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The axial symmetry of a railway wheel is taken into account to expand its vibrational response around the circumferential direction using Fourier series. This allows the vibroacoustic problem of the wheel to be formulated in a two-dimensional frame, solving for the dynamic and acoustic variables analytically in the circumferential direction. By adopting an Eulerian approach, the inertial effects associated with the rotation of the wheelset are included in the model, assuming a constant angular speed of rotation. To represent a railway wheelset, the wheel is constrained at the inner edge of the hub and the contribution of the rigid body motion of the wheelset is superimposed on its response. The latter is evaluated analytically under the assumption of small rigid body displacements. The computational efficiency of the proposed methodology is found to be three orders of magnitude greater than a full three-dimensional methodology, without compromising the accuracy. The results are compared in terms of acoustic radiation with the commercial package Ansys, showing similar sound power levels in almost all the frequency range apart from some differences at low frequencies due to the use of an acoustic model based on radiation ratios.

Around 35,000 km high-speed railways are in operation in China with a maximum speed of 350 km/h. The main track form on the high-speed lines is non-ballasted slab track. Measurements show that, at high speeds, rolling noise is still the dominant source for both interior and exterior noise. Although rolling noise modelling has been investigated for more than 30 years, a train running at 350 km/h or higher along a non-ballasted slab track introduces a number of new factors which have not been adequately addressed in the past. The aim of this paper is to describe an approach that brings together elements that have been developed recently to model rolling noise for a high-speed train running on a slab track. Features of the approach include modelling interactions between multiple moving and rotating wheelsets with an infinitely long periodic track, treating all the radiators as moving sources, and directly predicting sound pressure frequency spectra for observation points near the track. Results are produced for a typical Chinese high-speed train and track, including wheel andrail receptances, wheel/rail forces, comparison of rolling noise with measured pass-by noise, dependence on train speed, and contributions from the wheelset, rail and slab.

[EN] The noise inside railway vehicles is transmitted by both structure-borne and airborne paths and, although there are many sources, the rolling noise is often the most important. This paper focuses on the structure-borne transmission of rolling noise in a metro vehicle. Measurements are presented first of the vertical and lateral dynamic stiffness of a primary suspension element consisting of conical rubber/metal elements. Results are presented for various constant preloads over the frequency range 60600 Hz. An analytical model of the suspension element is also developed, based on a mass-spring system and including wave motion within the rubber elements. The dynamic stiffness results are used in a finite element model of the running gear, consisting of the bogie frame, wheelsets and suspension elements. The excitation is provided by the combined wheel/rail roughness at the contact point. This model is used to calculate the blocked forces at the connection points between the secondary suspension elements and the car body. The blocked forces are combined with measured vibro-acoustic transfer functions from these mounting points to the vehicle interior to determine the structure-borne noise inside the vehicle. The proposed methodology is validated against measurements during operation in terms of acceleration levels, blocked forces and structure-borne noise levels inside the vehicle, showing reasonably good agreement. Including the dynamic stiffness for the primary suspension leads to improved agreement between 100 and 500 Hz compared with using a constant stiffness., The work presented in this paper has received funding from the Shift2Rail Joint Undertaking under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 777564). The contents of this publication only reflect the authors' views and the Joint Undertaking is not responsible for any use that may be made of the information contained in the paper.

[EN] A framework is described for predicting the airborne noise inside railway vehicles which is applied to rolling noise sources. Statistical energy analysis (SEA) is used to predict the interior noise by subdividing the train cabin into several subsystems. The dissipation loss factors are obtained from the measured reverberation time in the train cabin. The power input to the interior SEA model is obtained from the external noise sources by multiplying the incident sound power on the external surfaces with measured transmission coefficients of the train floor and sidewalls. The sound power incident on the train floor is calculated by using an equivalent source model for the wheels and track together with an SEA model of the region below the floor. The incident sound power on the sides is obtained by using a waveguide boundary element (2.5D BE) method. The procedure is applied to a Spanish metro train vehicle running in the open field for which rolling noise is the main external noise source. The procedure is verified by field measurements of sound pressure beneath the carriage, on the sidewalls and inside the vehicle. The sensitivity of the results to changes in interior absorption is also studied, including the effect of passengers., 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 pape

Railway acoustic problems commonly have a constant cross-section and uniform properties in the longitudinal direction. To solve such 3D acoustic problems with reduced effort, a wavenumber domain acoustic finite element (2.5D acoustic FE) method is introduced in which the cross-section of the domain is meshed and the third dimension is represented by a wavenumber transform. The acoustic wavenumber is thereby decomposed into a combination of wavenumbers in the x direction and in the y-z plane. The method is extended to exterior noise problems by including a perfectly matched layer (PML) with bespoke absorption to prevent reflection of the sound waves at the boundary of the domain. The method as presented can be used with 2D finite element solutions from commercial software. To verify the application of the 2.5D acoustic FE method for interior acoustic problems, sound attenuation in a tunnel is predicted and compared with existing measurements. To verify the implementation for exterior acoustic problems, an example is given of the sound distribution on the side surface of a train due to a compact source below it. The comparison of the solutions obtained from the 2.5D acoustic FE models with measurements shows good agreement in the both validation cases. The method is then used to investigate the effect of the tunnel walls on the sound distribution on the train external surface by comparing the results with the case in the open field. A highly reverberant sound field is found in tunnels, which increases the sound pressure level on the train side-surface above 250 Hz by about 10 dB for a tunnel with a ballasted track and by about a further 6 dB for a slab track.

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.

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.

Curve squeal noise is a severe railway noise problem that can occur when a railway vehicle negotiates a sharp curve. It is usually characterised by a very loud tonal noise and can be very annoying for people in the vicinity. It is generally attributed to friction-induced instability, either due to a falling friction characteristic with increasing sliding velocity or to a mode coupling mechanism which can lead to instability even for a constant friction coefficient. The squeal frequency is usually associated with one or more wheel modes. However, the wheel is coupled dynamically to the track and insufficient attention has been paid in previous research to the role played by the rail dynamic behaviour. In this paper, the effect of the rail dynamics on curve squeal under constant friction conditions is investigated by means of different modelling approaches. The rail is firstly modelled using a waveguide finite element (WFE) model and it is found that the inclusion of the rail dynamics in the model can lead to squeal in some situations where it would otherwise not occur. Various effects are then considered that may introduce additional resonant behaviour into the rail dynamics. These include the effect of the rail cross mobility, rail cross-section deformation, the influence of the periodic support of the rail and reflections between multiple wheels on the rail. The effect of the rail pad stiffness is also explored. However, the results show that all these factors have little influence on the predicted curve squeal instabilities. By means of a reduced model, the main characteristics of the rail dynamics that can result in squeal are then assessed. It is shown that the mass and damping-like behaviour of the infinite rail are at the origin of the instabilities rather than any modal behaviour of the track. Curve squeal may occur for a single wheel mode even if the rail is represented by a damper, which is a close approximation to the vertical mobility of the track at high frequencies. This forms a third possible mechanism for curve squeal in addition to falling friction and wheel mode coupling.

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.

Aerodynamic noise from pantographs becomes an important source of noise from trains at high speeds. Previous studies have mostly been based on numerical predictions using computational aeroacoustic methods, which require large computing resources, or measurements conducted in a wind tunnel which cannot take all the real conditions into account. A component-based model relying on empirical constants obtained from the literature has been shown to predict aerodynamic noise from pantographs that agrees well with wind tunnel measurements. This model is extended in this paper by making use of simulation results on individual cylinders to refine the model constants and the Reynolds number dependence. In addition, allowance for the effect of incoming turbulence and cylinder aspect ratio is also extended. The updated model shows improved agreement with wind tunnel measurements, particularly at low frequencies. This model is then used to predict pantograph noise in more realistic conditions during train pass-by. The incoming flow conditions in terms of the incident flow speed, the turbulence intensity and the turbulence length scale are estimated from the literature considering the development of the boundary layer along the train roof. The sensitivity of the model to these assumptions is assessed using Monte Carlo simulations. The predicted results are compared with field measurements obtained using microphone array techniques for pantograph on different operational trains. Good agreement is obtained between the predictions and the measurements in terms of the far-field noise spectra and the dependence of noise level on speed. Differences are noted between measured levels for different orientations of the pantograph which according to the model are mainly related to the distance of the pantograph from the front of the train.

This paper is concerned with the prediction of the vibro-acoustic behavior of rib-stiffened panels treated with multiple layers of porous materials. The acoustically treated rib-stiffened panels are assumed to be uniform and infinitely long in one direction (the longitudinal direction) but the cross-section can have an arbitrary and often complicated shape. Although the two-and-half dimensional structural finite element method (2.5D FEM) and the two-and-half dimensional acoustic boundary element method (2.5D BEM) may be combined to perform the vibro-acoustic prediction, the presence of the multiple layers of acoustic treatment often makes the prediction too time-consuming. More efficient methods are required for such structures and the aim of this paper is to propose such a method. The rib-stiffened panel and the fluid domain containing the incident and reflected sound waves are modelled using 2.5D FEM-BEM while the acoustic treatment layer and the fluid domain containing the transmitted sound waves are dealt with, approximately, using the transfer matrix method (TMM). The coupling of TMM and 2.5D FEM-BEM is formulated in detail. Since the acoustically treated panel is assumed to be flat and baffled, the 2.5D BEM is based on the Rayleigh integral in the wavenumber domain. Meanwhile, the TMM is based on a two-dimensional Fourier transform which implies that the porous layers also extend to cover the baffle; the validity of this assumption is explored. The accuracy and efficiency of the method is compared with a full 2.5D FE-BE method for a homogeneous plate with attached layers of absorbent material. It is shown that the method proposed in this paper can reduce calculation time by about a factor of three compared with the full 2.5D FE-BE method. The proposed method is then applied to study the sound transmission loss (STL) of a typical rib-stiffened panel from a train carriage which is acoustically treated with different porous material layers, demonstrating that the design of the acoustic treatment can have a significant effect on the STL of the panel.

In predicting rolling noise from a railway wheelset, some assumptions are usually required to make the calculations less complicated and more efficient. In this study, the effects of some modelling assumptions on the prediction of sound power radiated from a high-speed train wheelset are investigated by using the finite element and boundary element methods. Use is made of the axi-symmetry of the wheelset to allow the solution to be obtained in terms of a Fourier series in the circumferential direction. Compared with a moving-wheel formulation, the moving-roughness approach is shown to be sufficient provided that the wheelset receptance takes into account the effects of rotation and the rail receptance accounts for the effect of the moving load. Wheel/rail coupling should take account of lateral as well as vertical forces; neglect of the lateral interaction may result in significant overestimates of the contribution of the axial modes of the wheelset, and thus the overall wheelset radiated noise. If the rotation of the wheelset is not considered, its radiated noise may be underestimated by up to 3 dB at frequencies above 2000 Hz. If the wheelset suspension is not included, the overall sound power would be overestimated at frequencies below 2000 Hz. Compared with symmetric excitation of the wheelset, assuming incoherent excitations for the left and right wheel/rail contacts will significantly affect the radiated noise in the frequency range below 2000 Hz but has negligible effect on the important region above 2000 Hz. Finally, the contribution from the axle is shown to be significant below 1000 Hz. In terms of overall A-weighted level, the effect of the lateral wheel/rail interaction, the rotation of the wheelset and the inclusion of bearings and axleboxes should not be neglected.

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.

[EN] In order to be able to predict train interior noise, it is first important to calculate the external sound pressure distribution on the floor, sidewalls and roof. This can then be combined with the transmission loss of the train panels to determine the interior noise. Traditional techniques such as the finite element and boundary element (FE/BE) methods in three dimensions (3D) can achieve this result but are computationally very expensive. In this paper, a wavenumber-domain boundary element (2.5D BE) approach is instead adopted to predict the propagation of rolling noise from the wheels, rails and sleepers to the train external surfaces. In the 2.5D models, only the cross-section of the vehicle is represented by using boundary elements, while the third direction is considered in terms of a spectrum of wavenumbers. The rail is treated directly in the wavenumber domain but, to include the wheel, a method of representing point sources in a 2.5D approach is developed. An inverse Fourier transform is applied to obtain the spatial distribution of the sound pressure on the train surfaces. The validity of this approach has been verified by comparison with experimental data. The 2.5D BE method was first used to predict the sound distribution on a 1:5 scale train surfaces due to a point source below the vehicle, and later it was used to predict the sound pressure on a full-scale metro vehicle due to a loudspeaker. Comparisons of predictions with measurements on the scale model and on the metro vehicle showed good agreements. For a point source below the vehicle, the sound pressure levels on the train floor were found to be around 20 dB higher than on the sides, and the sound pressure on the train roof was negligible. The 2.5D BE method was also used to predict the sound pressure on the metro vehicle surfaces in running operation, in which the predicted sound pressure levels on the train external surfaces agreed with measurements to within 3 dB and similar trends were found in terms of spectra and longitudinal distribution of pressure., The work presented in this paper has received funding from China Scholarship Council and the Shift2Rail Joint Undertaking under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 777564). The contents of this publication only reflect the authors' view and the 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. The authors are grateful to Dr. Xianying Zhang for providing the measured vibration of the 1:5 scale rail. All data published in this paper are openly available from the University of Southampton repository at 10.5258/SOTON/D1483

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.

A resonance pattern at frequencies from around 400 Hz to 1000 Hz has often been observed from measured rail accelerations. Such resonances are important for rail noise and corrugation. Although this pattern has been reported and discussed in several papers in terms of wave reflections between multiple wheels, the aim of this study is to investigate the generation mechanism of this resonance phenomenon in detail, and to give both mathematical and physical insight. An infinite Timoshenko beam with continuous supports is adopted for modeling the track system, and the point and transfer receptances of the rail for a stationary harmonic excitation are explicitly obtained by the residue theorem. A frequency-domain method is then presented to calculate the power spectral densities of the wheel-track coupled system responses to stochastic irregularities with the moving irregularity model. It is found that the multiple peaks can be explained by using the phase closure principle. Moreover, total reflection between the two wheels may occur at around 700 Hz, which results in the highest peak in the response.

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

This paper presents an investigation, using both numerical and experimental methods, of the application of spanwise waviness to reduce aerodynamic noise from square bars. The numerical simulations are performed using the Delayed Detached-Eddy Simulation approach to obtain the near-field unsteady flow properties, which are then used to calculate the equivalent source terms in the Ffowcs Williams-Hawkings equation for far-field noise prediction. For a straight square bar in cross-flow, which produces strong tonal noise associated with the vortex shedding, a benchmark study shows good agreement between numerical simulations and measurements in terms of far-field noise spectra. Waviness is then introduced along the bar span and the influence of the amplitude and wavelength of the waviness is studied. When the wave amplitude is nearly half the bar width, a large noise reduction of as much as 30 dB is found from both numerical simulations and measurements, including a 10 dB reduction in the broadband level. The influence of the wavelength is much smaller. Analysis of the flow features show that, with increased wave amplitudes, the spanwise flow becomes significant and strong crossflow vortices develop in the near wake which effectively suppress the primary vortex shedding. This reduces the noise level significantly, especially the tonal noise associated with the vortex shedding.

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 car body structures of modern trains are often formed of extruded aluminium panels. Their acoustic properties, particularly the sound transmission loss, have an important influence on the interior acoustic environment. In order to study the acoustic performance of extruded panels, their Sound Transmission Loss (STL) is studied using the coupled Wavenumber Finite Element method (WFE) and Wavenumber Boundary Element method (WBE). The damping of a typical structure is first measured in the laboratory to give suitable input values for the model. The predicted STL is compared with corresponding measurements of the sample panel, with good agreement above 400 Hz. Based on the validated model, an extensive parametric study is carried out to investigate the effect of different reinforcement rib styles on the STL. The effect of using extruded panels with rectangular, triangular and trapezoidal truss-core sections is studied in detail. Among the parameters studied, the number of bays in a given width has a great influence on the sound insulation. Considering practical use, both the mass and stiffness of each case are also considered. To give increased understanding of the STL behaviour, the dispersion curves are also studied. It is found that structures with better STL usually have fewer free wavenumbers below the acoustic wavenumber. For the same number of structural bays, a panel with triangular stiffening has the highest strength but also the largest mass, whereas a structure with rectangular stiffening has the least strength and lowest mass. In the evaluation, the weighted STL Rw and the spectral adaptation term Ctr are considered. The results are also considered relative to a mass law adjustment of the STL. It is found that the three cases which give the best results are a triangular rib panel with 4 or 5 bays in a 1 m width, and a trapezium case with 5 bays and inclination angle 25°. These have an Rw that is 2–6 dB better than the reference panel, a smaller mass and a higher stiffness.

Solid panels with additional poro-elastic materials are widely used in engineering, mainly for sound insulation. In many cases, the panels are constructed in such a way that they can be idealised to be infinitely long and uniform in one direction, forming a so-called two-and-a-half dimensional (2.5D) structure. Although the 2.5D finite element and boundary element methods (FEM-BEM) are particularly suitable for predicting the vibro-acoustic behaviour of such structures, up to now the presence of poro-elastic media have not been adequately considered. In this paper a 2.5D FE-BE vibro-acoustic model is presented which accounts for solids, fluids and poro-elastic media. The poro-elastic media are modelled using the 2.5D FE approach based on the mixed displacement-pressure formulation of Biot's theory. The solids are also modelled using the 2.5D FE method but based on the linear theory of elasticity. The internal fluids are modelled using the 2.5D FE method as well. For a flat panel, the external fluid on both sides of the panel can be modelled using the 2.5D BE method based on the Rayleigh integral. The coupling between the various sub-models is derived in detail. The accuracy of the model is demonstrated by applying it to simple multi-layered structures for which solutions can be produced using other well-established methods. It is demonstrated that the elasticity of the solid frame of a porous medium has a great influence on the vibro-acoustics of a structure containing the porous material. The method is then applied to investigate the sound transmission loss (STL) of a typical railway vehicle floor structure. Results show that STL can be greatly improved by proper arrangement of porous material layers between the interior wooden floor and the outer extrusion; however, the load bearing supporting beams may significantly reduce the benefit of the porous material layers.

In order to counteract the problem of railway noise and its environmental impact, passing trains in Europe must be tested in accordance to a noise legislation that demands the quantification of the noise generated by the vehicle alone. However, for frequencies between about 500 Hz and 1600 Hz, it has been found that a significant part of the measured noise is generated by the rail, which behaves like a distributed source and radiates plane waves as a result of the contact with the train's wheels. Thus the need arises for separating the rail contribution to the pass-by noise in that particular frequency range. To this end, the present paper introduces a wavenumber–domain filtering technique, referred to as wave signature extraction, which requires a line microphone array parallel to the rail, and two accelerometers on the rail in the vertical and lateral direction. The novel contributions of this research are: (i) the introduction and application of wavenumber (or plane–wave) filters to pass-by data measured with a microphone array located in the near-field of the rail, and (ii) the design of such filters without prior information of the structural properties of the rail. The latter is achieved by recording the array pressure, as well as the rail vibrations with the accelerometers, before and after the train pass-by. The performance of the proposed method is investigated with a set of pass-by measurements performed in Germany. The results seem to be promising when compared to reference data from TWINS, and the largest discrepancies occur above 1600 Hz and are attributed to plane waves radiated by the rail that so far have not been accounted for in the design of the filters. QC 20170801 Roll2Rail

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.

Models for predicting railway rolling noise such as TWINS are well-established and have been validated against field measurements. However, there are still some areas where improvements are required. In particular, the radiation from the rail is based on a model of a rail in free space whereas in reality the rail is located close to the ground; there are also limitations in the existing model for the sound radiation from the sleepers. Besides, the influence of the ballast absorption on the sound power radiated by the track is neglected. This paper draws on recent research into the effects of the proximity of the rail and sleeper to an absorptive ground on their sound radiation, based on the boundary element method. In reality, the rail is located above the ballast over part of its length, and attached periodically to the concrete sleepers elsewhere. The sound radiation of the rail for those two situations can be predicted using the 2D boundary element method. In order to obtain a realistic rail radiation model for engineering applications, a method to combine those two results is proposed and the resulting average rail radiation is verified by using a 3D boundary element model. An improved sleeper radiation model is also proposed and verified using the 3D boundary element model. These new engineering models for the rail and sleeper radiation have been used together with TWINS to predict the sound radiation from operational tracks and the results have been compared with field measurements. Compared with the TWINS model, the rail radiation is found to be increased below 300 Hz, but decreased above 1 kHz; the sound radiation from the sleeper is reduced compared with the TWINS model below 600 Hz.

Wheel–rail impact loads and noise at railway crossings are calculated by applying a hybrid prediction model. It combines the simulation of non-linear vertical dynamic vehicle‒track interaction in the time domain and the prediction of sound pressure level using a linear frequency-domain model. The two models are coupled based on the concept of an equivalent roughness spectrum. The time-domain model uses moving Green's functions for the linear vehicle and track models, accounting for wheel structural flexibility and a discretely supported rail with spatially-varying beam properties, and a non-Hertzian wheel–rail contact model. Three-dimensional surface geometry of the wheel and crossing is accounted for in the solution of the wheel–rail contact. The hybrid model is compared against field measurements and is demonstrated by investigating the influence of vehicle speed and crossing geometry on the radiated impact noise. Based on simulation results, it is concluded that the impact loads and noise can be mitigated by reducing the effective dip angle at the crossing, which is determined by the vertical trajectory of the wheel when making the transition between wing rail and crossing nose.

A numerical investigation of the aeroacoustic characteristics of the flow past a circular cylinder is presented for Reynolds numbers in the range 2.67×104−3.67×105, which falls within the upper subcritical and critical regimes. This is based on computational fluid dynamics simulations using a delayed detached-eddy simulation model for the aerodynamics of the near-field, which feeds the equivalent source terms into the Ffowcs Williams–Hawkings equation for far-field noise prediction. The accuracy of delayed detached-eddy simulation in predicting unsteady flow quantities is assessed from an engineering viewpoint through comparisons with experimental data. Good agreement is found for both the near-field flow quantities and the far-field noise spectra. The aerodynamic and aeroacoustic characteristics are investigated from two aspects: the effect of varying the Reynolds number and the sensitivity to the spanwise computational dimension. The results in terms of the vortex shedding frequency, hydrodynamic forces and far-field noise levels only show small variations in the subcritical range. However, in the critical range, the vortex shedding frequency increases and the noise level decreases considerably after allowing for the typical sixth power dependence. A spanwise length of 3D is found to be sufficient for most Reynolds numbers in the critical range; but in the subcritical range, a longer spanwise length is needed, and the sound level may be under-predicted by up to around 4.5 dB by using 3D.

Complex-shaped aluminium panels are adopted in many structures to make them lighter and stronger. The vibro-acoustic behaviour of these complex panels has been of interest for many years but conventional finite element and boundary element methods are not efficient in predicting their performance at higher frequencies. Where the cross-sectional properties of the panels are constant in one direction, which is the case for extruded panels, wavenumber domain numerical analysis can be applied and this becomes particularly suitable for panels with complex cross-sectional geometries. Because they are based on a two-dimensional model, these methods can reduce the computational cost compared with other numerical methods using full three-dimensional models, while nevertheless including three-dimensional effects. In this paper, a coupled waveguide finite element and boundary element method is applied to predict the radiation efficiency and sound transmission of a double-layered aluminium extruded panel from a train carriage floor. The results are interpreted in the wavenumber domain from which the contributions of different types of waves can be identified. In the calculations, the air cavities between top and bottom panels are considered to examine their contributions to the vibro-acoustic behaviour of the panel. The predicted results are compared with measured ones obtained using a finite length panel. To reflect the finite length of the actual panel used in the measurement, spatial window functions are applied to the sound transmission through the infinitely long panel, giving improved agreement with the measurements.

In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes more compact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are developed depending the basis function that represents the displacements associated with the deformation; these basis functions are: (1) the shape functions that are used in the three dimensional finite element (FE) method; (2) the undamped mode shapes of the solid; (3) the shape functions that are adopted in the axisymmetric FE approach. Comparisons are shown of calculations carried out using these models. These show the existence of modal veering when analysing the Campbell diagram for a railway wheel.

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.

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.

The sound radiation of a railway in close to proximity to a ground (both rigid and absorptive) is predicted by the boundary element method (BEM) in two dimensions (2D). Results are given in terms of the radiation ratio for both vertical and lateral motion of the rail, when the effects of the acoustic boundary conditions due to the sleepers and ballast are taken into account in the numerical models. Allowance is made for the effect of wave propagation along the rail by applying a correction in the 2D modelling. It is shown that the 2D correction is necessary at low frequency, for both vertical and lateral motion of an unsupported rail, especially in the vicinity of the corresponding critical frequency. However, this correction is not applicable for a supported rail; for vertical motion no correction is needed to the 2D result while for lateral motion the corresponding correction would depend on the pad stiffness. Finally, the corresponding numerical predictions of the sound radiation from a rail are verified by comparison with experimental results obtained using a 1/5 scale rail model in different configurations.

Many issues of concern in the railway industry are fundamentally caused by dynamic wheel-rail interaction. To deal with these issues, the characteristics of the interaction must be accurately predicted and fully understood; this becomes even more challenging when the train speed is high. Although much research has dealt with wheel-rail interaction, some aspects related to high speed trains still need to be further addressed. In this paper, an approach based on time-domain moving Green's functions developed previously is extended and employed to calculate wheel-rail forces. The extension includes consideration of the flexibility and rotation of the wheelset by incorporating the associated time-domain moving Green's functions in the method. These are derived from the corresponding receptances by applying an experimental modal analysis technique to the calculated frequency response functions. Cases are considered for a single, or multiple, wheelsets rolling over a track represented as an infinitely long periodic structure. Wheel-rail forces are calculated for a set of parameters typical of the Chinese high-speed railway and for a number of typical excitation cases, including purely parametric excitation on a smooth rail, an indentation on the rail, wheel polygonisation and rail corrugation, for the purpose of revealing the frequency content of high-speed wheel-rail interaction. Effects of the wheel rotation on the wheel-rail forces are studied and comparisons are made between a single wheelset and multiple wheelsets.

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.

It is generally considered that a Timoshenko beam is superior to an Euler-Bernoulli beam for determining the dynamic response of beams at higher frequencies but that they are equivalent at low frequencies. Here, the case is considered of the parametric excitation caused by spatial variations in stiffness on a periodically supported beam such as a railway track excited by a moving load. It is shown that large differences exist between the results obtained using Timoshenko and Euler-Bernoulli beams for a railway track with typical parameters; the Euler-Bernoulli beam model underestimates this parametric excitation by around a factor of 3. This difference is shown to be due to shear deformation in the rail, which is significant for span lengths less than about 2 m. A 2.5D finite element model of the rail is used as a reference. This gives a deflection that is closer to the Timoshenko beam model. However, the displacement profile obtained from the Timoshenko beam model has a discontinuity of gradient at the support points, whereas neither the Euler-Bernoulli beam nor the 2.5D finite element model contains the discontinuity of gradient. Finally, the moving load is introduced explicitly in the various periodically supported models. The results for a moving constant load, expressed as an equivalent roughness, are not strongly affected by the load speed until the sleeper passing frequency approaches the vertical track resonance at which the track mass bounces on the support stiffness. Consequently, a quasi-static model gives satisfactory results for moderate load speeds.

Internal resonances in suspension springs can result in significantly increased vibration transmission at the corresponding natural frequencies. Particularly for the case of metal coil springs used in vehicle suspensions, these internal resonances can be as low as 50 Hz and can lead to increased structure-borne noise in certain frequency bands. Although, in practice, this can be mitigated to some extent by using rubber pads in series with the coil springs, high vibration transmission in the vicinity of the internal resonance frequencies remains an important issue. In this paper, a mechanism is identified that can overcome the increased vibration transmission due to the internal resonances. This involves the use of a pivoted arm with a pivot bushing that is relatively stiff for translational motion. The quasi-static load is primarily carried by the suspension spring but the dynamic load at higher frequencies is also transmitted through the pivot bushing. By appropriate selection of parameters, in particular the moment of inertia of the pivoted arm and the stiffness of the pivot bushing, it can be arranged that the dynamic loads acting through the spring and the bushing largely cancel each other out at the spring natural frequency. It is shown that this mechanism is contained within common designs of railway vehicle primary suspension. Nevertheless, their design is largely based on their quasi-static behaviour and this principle of dynamic load cancellation has not previously been explained. The dynamic behaviour of different suspension arrangements is compared and the selection of suitable parameter values that can achieve this dynamic load cancellation is explained. Field measurements are also presented which confirm this behaviour.

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.

In most previous studies of sound radiation from railway rails, the rail has been regarded as located in free space, disregarding the influence of the ground. However, in order to predict the noise from the rail more precisely, the effect of the ground should be included in rolling noise predictions. In this study, the rail noise is investigated by means of a wavenumber domain numerical method, including the presence of the ground. For rails attached to a rigid ground or located at a certain distance above it, the influence of the ground is examined in terms of the radiation ratio and longitudinal directivity. From the prediction of radiated power, it is found that the vertical and lateral bending waves of the rail radiate most of the noise for the corresponding direction. Hence, a simplified calculation is proposed that only includes these waves, instead of a full three-dimensional analysis. An absorptive ground is also modelled by applying impedance boundary conditions at the ground surface to investigate the influence of the ground on the rail noise. Finally, for the vertical and lateral bending waves in the rail, the cross-sectional directivity of the noise is predicted for various surface impedances of the ground. It is found that the simplified calculation proposed in this study is valid for the prediction of noise from the rail. Also the presence of the ground and its impedance condition have considerable effects on the level and directivity patterns of the noise radiated from the rail.

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.

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 reciprocity principle is well-known and has many applications in acoustics and vibro-acoustics. This paper discusses a reciprocity measurement method to determine the radiation efficiency of a vibrating structure. The method comprises two steps: (i) measurements of the acceleration response of the structure induced by a sound field in a reverberation chamber and (ii) measurements of the spatially-averaged squared transfer mobility of the structure. The approach is more flexible than a direct method and has the advantage that no shaker is required to excite the structure in the acoustic measurements. To demonstrate the applicability of this method, experiments were conducted on rectangular flat plates, on two components of a railway track test-rig and on three different built-up structures. For the plates and the railway rig components, comparisons are also made with theoretical models. It is shown that the measured results for each arrangement obtained using this reciprocity method provide good agreement with conventional direct measurements and with theoretical modelling. However, in most of the examples presented, the direct method has been found to be less practical and sometimes even less accurate than the reciprocal one, mostly due to the structure-shaker connection and to the inherent uncertainty of acoustic intensity measurements.

Some beam-like structures such as a railway track are effectively infinite in nature. Analytical solutions exist for simple structures but numerical methods like the finite element (FE) method are often employed to study more complicated problems. However, when the FE method is used for structures of infinite extent it is essential to introduce artificial boundaries to limit the area of computation. Here, a non-reflecting boundary is developed using a damped tapered tip for application in a finite element model representing an infinite supported beam. The FE model of the tapered tip is validated against an analytical model based on Bessel functions. The reflection characteristics of the FE tapered tip are quantified using a wave/FE superposition method. It is shown that the damped tapered tip is much more effective than its constant counterpart and achieves reduction of the model size. The damped tapered tip is applied to a simple FE railway track model and good agreement is found when its point mobility is compared with an analytical infinite track model.

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.

At typical speeds of modern high-speed trains the aerodynamic noise produced by the airflow over the pantograph is a significant source of noise. Although numerical models can be used to predict this they are still very computationally intensive. A semi-empirical component-based prediction model is proposed to predict the aerodynamic noise from train pantographs. The pantograph is approximated as an assembly of cylinders and bars with particular cross-sections. An empirical database is used to obtain the coefficients of the model to account for various factors: incident flow speed, diameter, cross-sectional shape, yaw angle, rounded edges, length-to-width ratio, incoming turbulence and directivity. The overall noise from the pantograph is obtained as the incoherent sum of the predicted noise from the different pantograph struts. The model is validated using available wind tunnel noise measurements of two full-size pantographs. The results show the potential of the semi-empirical model to be used as a rapid tool to predict aerodynamic noise from train pantographs.

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