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Steel coil springs are commonly used in the primary suspension of rail vehicles, usually in the form of two concentric springs. They exhibit strong internal resonances, which can lead to high vibration amplitudes within the spring itself. In some metro vehicles, large numbers of spring failures have occurred due to fatigue fracture in working conditions. The cause of these failures is investigated by studying the vehicle/track interaction, the modal response of the coil springs and the stresses occurring within them in working conditions. A finite element model is used to determine the modal parameters of the primary suspension. The resulting dynamic stiffness matrix is then included in a multi-body vehicle model and coupled to a model of the track. This coupled model is used to investigate the effect of the dynamic properties of both the springs and the track on the stresses in the springs. The springs exhibit strong internal resonances at around 50-60 Hz, at which very large stresses occur in both springs. This frequency range coincides with the P2 resonance frequency (wheelset mass bouncing on the track stiffness) for the standard slab track system used on this metro system. For other track systems, the P2 resonance occurs at a different frequency and the stresses are lower. These results are confirmed with field test data. From the stresses the weakest position in the inner spring is identified, which is found to correspond to the position of common breakages found in field observations. Some guidelines are proposed for reducing the vibration and stress, so that the fatigue fracture incidents can be reduced.

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...

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.

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.

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

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.

Aerodynamic noise is a significant source for high-speed trains but its prediction in an industrial context is difficult to achieve. In this article, the flow and aerodynamic noise behaviour of a simplified high-speed train bogie at scale 1:10 are studied through numerical simulations. The bogie is situated in a cavity beneath the train and the influence of a bogie fairing on the flow and flow-induced noise that developed around the bogie area is investigated. A two-stage hybrid method is used, which combines the computational fluid dynamics and an acoustic analogy. The near-field unsteady flow is obtained by solving the unsteady three-dimensional Navier–Stokes equations numerically using delayed detached-eddy simulation, and the data are utilised to predict the far-field noise based on the Ffowcs Williams–Hawkings acoustic analogy. Results show that when the bogie is located inside the bogie cavity, the shear layer developed from the leading edges of the cavity interacts strongly with the flow separated from the upstream components of the bogie and the cavity walls. Therefore, a highly turbulent flow is generated within the bogie cavity due to the strong flow impingements and flow recirculations occurring there. For the case without the fairing, the surface shape discontinuity in the bogie cavity along the carbody sidewalls generates strong flow unsteadiness around these regions. When the fairing is mounted in front of the bogie cavity, the flow interactions between the bogie cavity and the outer region are reduced and the development of turbulence outside the fairing is greatly weakened. Based on the predictions of the noise radiated to the trackside using a permeable data surface parallel to the carbody sidewall, it has been found that the bogie fairing is effective in reducing the noise generated in most of the frequency range, and a noise reduction of around 5 dB is achieved in the farfield for the current model case.

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.

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.

An investigation is presented of the use of finite element models in the time domain to represent a load moving on a railway track on a flexible ground. A systematic study is carried out to compare different sizes and shapes of finite element mesh, different boundary conditions intended for suppressing reflections from the truncated model boundaries, and different models of soil damping. The purpose is to develop guidance to assist in selecting appropriate finite element models for moving load problems. To prevent reflections from the boundaries of the finite domain two approaches are compared. A 40 m radius hemispherical finite element mesh has been used first with infinite elements around the perimeter. This approach gives good results for a point harmonic load at the centre of the domain but some problems are highlighted when it is used for moving load calculations. An alternative approach has therefore been investigated based on a cuboid mesh. The base was fixed to prevent rigid-body motions of the model and, rather than use infinite elements at the sides, these were also fixed. It is shown that, provided that a suitable damping model is used, the spurious reflections from the sides of the model can be suppressed if the model is wide enough. On the other hand, if infinite elements are used, the calculations are found to be considerably more costly with little added benefit. Different models of soil damping are also compared. It is shown that a mass-proportional damping model gives a decay with distance that is independent of frequency, making it particularly suitable for this application. The length of model required to achieve steady state has been investigated. For a homogeneous half-space it is found that the required length increases considerably in the vicinity of the critical speed, up to 130 m in the present example, whereas for the layered ground a more modest length is sufficient for all speeds.

Aerodynamic noise can be a significant problem in the operation of high-speed trains; its prediction is difficult to achieve in an industrial context. The aerodynamic and aeroacoustic behaviour of the flow past a simplified high-speed train bogie at scale 1:10 is studied in this paper; the utilized approach is a two-stage hybrid method that consists in computational fluid dynamics and computational acoustics studies. The near-field unsteady flow was obtained by numerically solving the Navier–Stokes equations with the delayed detached-eddy model and the results were used to predict the far-field noise using the Ffowcs-Williams – Hawkings method. The sound radiated from the same scaled bogie model was measured in an anechoic open-jet wind tunnel. The aeroacoustic characteristics of tandem wheelsets were also investigated for comparison purposes. It was found that the unsteady flow past the bogie is characterized by coherently alternating vortex shedding from the axles and more randomly distributed vortices of various scales and orientations from the wheels and frame. The vortices formed behind the upstream geometries move downstream due to convection and impinge on the downstream bodies, generating a highly turbulent wake behind the bogie. The noise predictions correspond fairly well with the experimental measurements for the dominant frequency of tonal noise and the shape of spectra. Vortex shedding from the axles generates tonal noise, with the dominant peak corresponding to the vortex-shedding frequency. The directivity exhibits a dipole shape for the noise radiated from the bogie. Compared with the wheelsets of the bogie, the noise contribution from the bogie frame is relatively weak.

It is generally accepted that track support stiffness is a major factor controlling rates of track geometry deterioration, particularly where the track support stiffness changes abruptly. There is, therefore, considerable potential benefit in being able to quantify and detect changes in the track support stiffness. In recent years, trackside techniques using various types of transducers have been developed to determine track deflections as trains pass. However, deducing the track support stiffness from these measurements requires assumptions to be made concerning train loading and track behaviour, and the possibility of different interpretations remains. For example, loads from moving trains vary dynamically and it is not usually feasible to measure their exact values at any given point along the track. This paper presents new methods of analysis, which can be applied to frequency spectra of track displacement, velocity or acceleration generated as trains pass to calculate the track support stiffness for trains of known axle intervals, without needing to know the actual loads applied. The approach is demonstrated with reference to theory and measured data from a range of field sites.

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.

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)

Quantifying how railway track responds to passing trains in terms of displacement, velocity or acceleration, can provide insights into both the performance and the condition of the track. A number of trackside monitoring technologies have been shown to be capable of providing this information; however these are primarily research tools and tend to be costly hence actual deployments are relatively limited in scope. To assess systematically the changing health of railway track, more cost-effective continuous approaches to monitoring are required. Micro electrical mechanical systems (MEMS) are commonplace sensors in consumer electronics, low cost and can be used to measure acceleration. Thus they have the potential to provide the kind of data required to assess railway track behaviour at a much lower cost and in an environmentally robust small deployment package. However confidence in the quality of the data is required. This paper discusses the criteria for the selection of MEMS devices for this application. Laboratory trials and direct comparison of trackside measurements with well-established monitoring techniques demonstrate the effectiveness of the selected MEMS devices, and show their potential for use in continuous monitoring schemes to evaluate changes in track performance. The paper thus provides evidence that these kinds of low cost technologies are suitable for railway applications, building confidence in their use and enabling their adoption in self-monitoring smart infrastructure.

[EN] This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel-rail contact is assumed to be flexible. The technique is based on the discretization of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track., This work was supported by the financial contribution of the European Union’s Shift2Rail programme (RUN2Rail project, grant number 777564), the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (projects TRA2013-45596-C2-1-R and TRA2017-84701-R).

A fully framed system consisting of four beams and a rectangular plate has been investigated in terms of the energy transfer between the beams and the plate when a force is applied to one of the beams. This configuration, which is a mixture of stiff and flexible elements, is a particularly important example in the industrial area, as it is widely used. A modal model based on interface basis functions is used. A wave model, which is an approximate method, has also been developed in which the plate, acting as a wave impedance, is separately attached to each beam. Experimental studies have been carried out for validation. The investigation with respect to power flow and energy shows the validity of both models in the mid-frequency region. The results show that most energy is dissipated by the flexible plate. The physical phenomena and limitations of the wave method for this particular structural configuration are discussed. Even though it is an approximate method, the wave approach can describe the dynamic characteristics of the excited beam and the plate in terms of the ratios of power and energy of each component. The comparison of the two methods shows that the plate rather than the beams plays a crucial role in transferring the energy from the excited beam to the parallel opposite beam in the beam-framed structure when these two beams have identical properties, whereas the energy transfer is reduced when the beams have dissimilar properties.

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

At speeds above 300–350 km/h, the main source of noise from trains is the aerodynamic noise caused by the air flow over the train structure. The sound level increases with train speed at a rate of between 60 and 80 times the logarithm of the speed so that, as speeds increase further, the noise increases dramatically. The main aerodynamic noise is produced by the air flow passing over the pantograph, the train nose, the bogie region and cavities such as the pantograph recess and the inter-coach gap. Experimental and numerical methods for studying aerodynamic noise are reviewed including the use of microphone arrays, wind tunnels, computational fluid dynamics and semi-empirical methods. Potential mitigation measures that can control aerodynamic noise are also reviewed.

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.

Rail corrugation occurring on tracks fitted with Egg fasteners has become a serious problem on the newly operated lines of the Beijing metro in recent years. Investigations and field measurements show that the dominant wavelengths of corrugation are 63–100 mm, inducing dominant frequencies of vibration on the rail in the frequency range of 160–310 Hz for train speeds at 60–70 km/h. Due to the influence of the dynamic behaviour of tracks on the formation of rail corrugation, various options for changing the dynamic behaviour of the track structure can be considered as possible solutions to treat corrugation. Four treatment measures have been considered: rail grinding, adding a rubber pad within the fastener, replacing the fastener with a compression-type fastener, and installing rail dampers on the rail. Field experiments have been carried out to evaluate the effectiveness of these rail corrugation treatment measures on two lines of the Beijing metro. Frequency response functions, track decay rates, and pass-by acceleration on the rail were measured, and the development of rail roughness was monitored. Experimental results show that all the four measures are effective to control or at least slow down the development of rail corrugation on tracks with Egg fastener. Rail grinding is mostly used to limit the effects of corrugation; here, it was noted that low-amplitude corrugation on some straight lines did not reappear after rail grinding. After adding a rubber pad within the fastener, the existing corrugation reduced in amplitude, while corrugation did not reappear on a newly ground rail. Replacing the fastener with a compression-type fastener and installing rail dampers on the rail were found to slow down the development of corrugation.

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

Railway impact noise is caused by discrete rail or wheel irregularities, such as wheel flats, rail joints, switches and crossings. In order to investigate impact noise generation, a time-domain wheel/rail interaction model is needed to take account of nonlinearities in the contact zone. A nonlinear Hertzian contact spring is commonly used for wheel/rail interaction modelling but this is not sufficient to take account of actual surface defects which may include large geometry variations. A time-domain wheel/rail interaction model with a more detailed numerical non-Hertzian contact is developed here and used with surface roughness profiles from field measurements of a test wheel with a flat. The impact vibration response and noise due to the wheel flat are predicted using the numerical model and found to be in good agreement with the measurements. Moreover, compared with the Hertzian theory, a large improvement is found at high frequencies when using the detailed contact model.

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.

This paper discusses the isolation performance of a laminated rubber-metal spring. A multi-degree-of-freedom-system model using mass-damper-spring components is developed to calculate its transmissibility due to only axial vibration in the spring. The results show the embedded layers of metal plate can improve the transmissibility at high frequency.

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,...

Aerodynamic noise becomes a significant noise source at speeds normally reached by high-speed trains. The train bogies are identified as important sources of aerodynamic noise. Due to the difficulty to assess this noise source carrying out field tests, wind tunnel tests offer many advantages. Tests were performed in the large-scale low-noise anechoic wind tunnel at Maibara, Japan, using a 1/7 scale train car and bogie model for a range of flow speeds between 50, 76, 89 and 100 m/s. The dependence of the aerodynamic noise from the bogie region on different factors has been studied for different bogie configurations and inflow conditions representing different positions of the bogie along the train. The speed dependence and the noise directivity have also been assessed. The results show the particular importance of the components exposed to the free flow, whereas those shielded within the bogie cavity are shown to radiate much less noise.

This paper compares the sound power and vibration levels for two different soundboards for upright pianos. One of them is made of laminated spruce and the other of solid spruce (tone-wood). These differ also in the number of ribs and manufacturing procedure. The methodology used is defined in two major steps: (i) acoustic power due to a unit force is obtained reciprocally by measuring the acceleration response of the piano soundboards when excited by acoustic waves in reverberant field; (ii) impact tests are adopted to measure driving point and spatially-averaged mean-square transfer mobility. The results show that, in the mid-high frequency range, the soundboard made of solid spruce has a greater vibrational and acoustic response than the laminated soundboard. The effect of string tension is also addressed, showing that is only relevant at low frequencies.

A trench can act as a barrier to ground vibration and is a potential mitigation measure for low frequency vibration induced by surface railways. However, to be effective at very low frequencies the depth required becomes impractical. Nevertheless, for soil with a layered structure in the top few metres, if a trench can be arranged to cut through the upper, soft layer of soil, it can be effective in reducing the most important components of vibration from the trains. This study considers the possibility of using such a realistically feasible solution. Barriers containing a soft fill material are also considered. The study uses coupled finite element / boundary element models expressed in terms of the axial wavenumber. It is found to be important to include the track in the model as this determines how the load is distributed at the soil's surface which significantly affects the insertion loss of the barrier. Calculations are presented for a range of typical layered grounds in which the depth of the upper soil layer is varied. Variations in the width and depth of the trench or barrier are also considered. The results show that, in all ground conditions considered, the notional rectangular open trench performs best. The depth is the most important parameter whereas the width has only a small influence on its performance. More practical arrangements are also considered in which the sides of the trench are angled. Barriers consisting of a soft fill material are shown to be much less effective than an open trench but still have some potential benefit. It is found that the stiffness of the barrier material and not its impedance is the most important material parameter. 2016 Elsevier Ltd. The results presented in this paper have been obtained within the EU FP7 project RIVAS (Railway Induced Vibration Abatement Solutions) under grant agreement No. 26575 . The project coordinator was UIC (International Union of Railways). The sixth and seventh authors are post-doctoral fellows of the Research Foundation Flanders (FWO). The financial support is gratefully acknowledged. All data published in this paper are openly available from the University of Southampton repository at http://dx.doi.org/10.5258/SOTON/394807 . Scopus

Demand forecasts for the medium to long term are essential to the successful planning and delivery of major airport infrastructure but the track record of airport demand forecasting appears to be mixed. The first priority area is therefore to improve forecasts and the report puts forward four key recommendations: Use quantitative methods to analyse the key drivers of airport demand. Use expert guidance to help interpret the quantitative results. Quality-assure the analysis and counter the risks of optimism bias. Reflect the risks and uncertainties that arise in even the best forecasts. The second priority is to make effective use of demand forecasts in airport infrastructure planning. The main purpose of recognising and quantifying risks and uncertainties in future airport demand is to help to develop useful risk management measures. Approaches divide into two broad groups: Risk sharing arrangements. Flexible strategic/dynamic strategic/adaptive planning. Thirdly, it is important to recognize that however successfully all of the foregoing is carried out, there are likely to remain material risks and uncertainties in even the best airport demand forecasts. The challenge is thus to make the residual uncertainty apparent to decision-makers without undermining the value attached to the economic appraisal of prospective investments.

Flow induced noise increase significantly with speed, consequently noise reduction has become an important consideration for high-speed train designs. However, reducing noise from a train pantograph is more challenging because of the difficulty to shield it using rail side acoustic barriers. The flow behavior around a high-speed pantograph arm and train roof at a 1/10 scale is investigated using computational fluid dynamics. The geometries of the roof and the pantograph arm are simplified as a square shallow cavity and a straight cylinder, respectively. To resolve the details of the turbulent flow structures and hence enable accurate noise predictions, the improved delayed detached-eddy simulation is used in near-field modelling and Ffowcs-Williams & Hawkings aeroacoustics model is employed for far-field acoustic calculation. In this work, the influence of geometrical alteration at the cavity leading edge is considered. The results show that the recirculation vortices, which generate highly turbulent flow, decrease with increasing cavity leading edge roundness, and this reduces wall pressure fluctuations, which is a major noise source, on the cavity and cylinder surfaces. Furthermore, aerodynamics performance, such as drag, is improved. Finally, the effect of the arm positions is studied. No significant effect was found for overall sound pressure level, but tonal noise levels from the cylinder was reduced. A reduction of interaction between the lower part of the cylinder surface and cavity shear layers was detected, and it is believed that the reduction of interaction reduces the peak noise levels.

The sleepers supporting the rails of a railway track are an important source of noise at low frequencies. The sound radiation from the sleepers has been calculated using a three-dimensional boundary element model including the effect of both reflective and partially absorptive ground. When the sleeper flexibility and support stiffness are taken into account, it is found that the radiation ratio of the sleeper can be approximated by that of a rigid half-sleeper. When multiple sleepers are excited through the rail, their sound radiation is increased. This effect has been calculated for cases where the sleeper is embedded in a rigid or partially absorptive ground. It is shown that it is sufficient to consider only three sleepers in determining their radiation ratio when installed in track. At low frequencies the vibration of the track is localised to the three sleepers nearest the excitation point whereas at higher frequencies the distance between the sleepers is large enough for them to be treated independently. Consequently the sound radiation increases by up to 5 dB below 100 Hz compared with the result for a single sleeper whereas above 300 Hz the result can be approximated by that for a single sleeper. Measurements on a 1/5 scale model railway track are used to verify the numerical predictions with good agreement being found for all configurations.

Vortex shedding from cylinders has been extensively studied due to its occurrence in many engineering fields. Many experimental studies reported in the literature focus on the aerodynamics of the vortex shedding process but the literature about the radiated noise is more scarce. The aim of the work presented here is to extend the available noise data. Aero-acoustic wind tunnel tests were carried out using cylinders with different cross-sections: circular, square, rectangular and elliptical. Flow speeds between 20 and 50 m/s were used, corresponding to Reynolds numbers in the range from 1.6×104 to 1.2×105. The dependence of the noise on the yaw angle, flow speed, cross-sectional shape, angle of attack and radiation angle (directivity) is assessed. The results obtained are compared, where possible, with those found in the literature for similar cases. It is intended that the results can be used for the validation and calibration of numerical and empirical aerodynamic noise prediction models.

Helical springs within the primary suspension are critical components for isolating the whole vehicle system from vibration generated at the wheel/rail contact. As train speeds increase, the frequency region of excitation becomes larger, and a simplified static stiffness can no longer represent the real stiffness property in a vehicle dynamic model. Coil springs in particular exhibit strong internal resonances, which lead to high vibration amplitudes within the spring itself as well as degradation of the vibration isolation. In this paper, the dynamic stiffness matrix method is used to determine the dynamic stiffness of a helical spring from a vehicle primary suspension. Results are confirmed with a finite element analysis. Then the spring dynamic stiffness is included within a vehicle-track coupled dynamic model of a high speed train and the effect of the dynamic stiffening of the spring on the vehicle vibration is investigated. It is shown that, for frequencies above about 50 Hz, the dynamic stiffness of the helical spring changes sharply. Due to this effect, the vibration transmissibility increases considerably which results in poor vibration isolation of the primary suspension. Introducing a rubber layer in series with the coil spring can attenuate this effect.

Models of rolling contact are used to predict the wear of the railhead due to passing wheels. It is commonly assumed in such models that material is worn away in proportion to the frictional work done in the slip zone of each contact patch. Moreover, a constant coefficient of friction is usually assumed. However, it is known that the friction coefficient between sliding surfaces decreases as the velocity of sliding increases. This paper describes a technique for including more sophisticated friction laws in a model of wheel–rail rolling contact. A non-Hertzian model is used based on a variational method. The resulting tangential stress distribution and slip velocity in rolling contact are examined and compared with results calculated using a constant coefficient of friction. For conditions of rolling contact with partial slip a stick–slip oscillation is found to occur when a velocity-dependent friction law is used. The pattern of material removed along the rail in rolling contact is also investigated. For...

The effect of unsupported sleepers on the dynamic behaviour of a railway track is studied based on vehicle-track dynamic interaction theory, using a model of the track as a Timoshenko beam supported on a periodic elastic foundation. Considering the vehicle's running speed and the number of unsupported sleepers, the track dynamic characteristics are investigated and verified in the time and frequency domains by experiments on a 1:5 scale model wheel-rail test rig. The results show that when hanging sleepers are present, leading to a discontinuous and irregular track support, additional wheel-rail interaction forces are generated. These forces increase as further sleepers become unsupported and as the vehicle's running speed increases. The adjacent supports experience increased dynamic forces which will lead to further deterioration of track quality and the formation of long wavelength track irregularities, which worsen the vehicles' running stability and riding comfort. Stationary transfer functions measurements of the dynamic behaviour of the track are also presented to support the findings.

The vibration of railcar wheels and rails due to excitation forces creates rolling noise. Microphone array measurements and theoretical models, such as the Track-Wheel Interaction Noise Software (TWINS) have been widely used to increase understanding of rolling noise. However, the array measurements are often inconsistent with the TWINS predictions and give less prominence to the rail than the TWINS models. This paper examines whether the microphone array measurements give a correct estimate of sound power radiated by the rail. Static tests are conducted to investigate the vibratory behavior of the track by using a hammer excitation. The sound radiation from a vibrating rail then is modeled with an array of monopole sources, whose strengths are assigned according to the rail vibration calculated using a Timoshenko beam model for the track. The radiation properties of the rail are examined using a shaker excitation in order to validate the sound radiation model. Simulations are used to identify the extent to which the microphone array could see the rail radiation. Results showed that a horizontal microphone array focused normal to the rail cannot detect a large part of the noise from the rail in high frequency range where free wave propagation occurs in the rail. Results obtained by using microphone arrays do not reflect the radiation characteristics of the noise from a rail. This causes the contribution of the rail component to noise to be underestimated.

The radiation efficiency of a flat rectangular plate is often used as a basis on which to represent the sound radiation from more complex plate-like structures. The solution for a plate set in a rigid baffle is well known, including the radiation efficiency for multi-modal response of the plate. In this case the assumption is usually made that each mode within a given frequency band has equal modal vibration energy. This paper explores a number of limitations of this simple result. First, the extent to which the radiation efficiency for a particular forcing point deviates from the modal-average result is investigated. Second, the difference is shown between the results for a baffled plate and an unbaffled plate. For a multi-modal response, an empirical formula is also presented which allows the radiation efficiency to be estimated for the unbaffled case. Finally, the effect of different boundary conditions on both baffled and unbaffled results is demonstrated by comparing the results for guided boundaries with those for simply supported boundaries.

Structural waves propagating along a railway rail form an extended source of sound radiation. Using an equivalent source model the distribution of this sound in a horizontal plane is investigated and shown to consist mainly of sound propagation at a particular angle to the normal. This direction is determined by the ratio of the wavenumbers in the rail and in air. Due to the extended nature of the rail as a source, the spatial distribution of the sound field in the direction along the track does not lend itself to the use of a simple directivity factor. The consequences for the measurement of noise from the rail using a microphone array are then explored. It is shown that a microphone array focussed normal to the rail does not detect most of the sound radiated by the rail. By turning the focus angle, the sound detected becomes a maximum when this angle corresponds to the angle of propagation of the sound radiation. Measurements on a test track using artificial excitation and measurements during the passage of a train confirm these conclusions.

Trains running on railway tracks on the surface of the ground or in tunnels induce vibrations in the ground which propagate away from the track. These may be experienced as feelable vibration or as audible rumbling noise in the buildings nearby, both of which are difficult to control. As the properties of the ground differ widely between locations they must be characterized for a particular site in order to make reliable predictions. This article describes field measurements of the vibration at two sites with soft clay soil in Southern England. The properties of the ground material, including its layered structure, have been identified from comparisons between results of a layered ground model and measurements obtained using impact excitation. Presentation in the wavenumber-frequency domain is particularly helpful for this purpose. Measurements of vibrations from passing trains are then compared with predictions using a semianalytical model for ground vibration from trains and good agreement is found.

Pre-assembled turnouts have recently been introduced with split concrete sleepers joined by elastic coupling plates. Their effect on the forces, vibration response, and sound radiation as trains run through a turnout is studied here using a calculation model for a whole turnout based on the finite-element method. The non-linear characteristics of the ballast's support under the sleepers, as well as the special construction of the articulated joints, are included. It is shown that compared with the normal integral sleeper design, the track with articulated switch sleepers has a lower rigidity, which changes more evenly along the track and improves its dynamic performance. Furthermore, the fatigue strength of an articulated switch sleeper is higher due to its lower stress amplitudes. Additionally, when the vehicles are running on the main turnout route, as the switch sleepers’ vibration behaviour is modified, the articulated joints effectively reduce the impact loading of the ballast at the end of the sleeper under the turnout branch track. This will extend the life of the ballast bed. Finally, the sound radiation from the articulated switch sleeper is very low in the hinged short part and is reduced by about 0.6 dB for the total length.