Ground-borne vibration due to static and dynamic axle loads of InterCity and high-speed trains

In predictions of railway-induced vibrations, a distinction is generally made between the quasi-static and dynamic excitation. The quasi-static excitation is related to the static component of the axle loads. The dynamic excitation is due to dynamic train–track interaction, which is generated by a large number of excitation mechanisms, such as the spatial variation of the support stiffness and the wheel and track unevenness. In the present paper, the quasi-static excitation and the dynamic excitation due to random track unevenness are evaluated by means of numerical predictions. A solution strategy is presented that allows for the evaluation of the second-order statistics of the response due to dynamic excitation based on the power spectral density function of the track unevenness. Due to the motion of the train, the second-order statistics of the response at a fixed point in the free field are non-stationary and an appropriate solution procedure is required. The quasi-static and dynamic contribution to the track and free-field response are analysed for the case of InterCity and high-speed trains running at a subcritical train speed. It is shown how the train speed affects the quasi-static and dynamic contribution. Finally, results of numerical predictions for different train speeds are compared with field measurements that have been performed at a site along the high-speed line L2 Brussels–Köln within the frame of homologation tests.     

Theoretical modeling and characteristic analysis of moving-train induced ground vibrations

An integrated train-track-subsoil dynamic interaction model of moving-train induced ground vibration is developed on the basis of vehicle dynamics, track dynamics and the Green's functions of subsoil. The model takes account of the vibrations of vehicle components, the quasi-static axle loads and the dynamic excitations between the wheels and track. The analyzed results from an example show that the ground vibration characteristics have a close relationship with train speed and soil properties; the dynamic responses excited by wheel-track irregularity have big influence on the high frequency components of ground vibration; with the increase of distance to the track, the ground acceleration has the tendency of decrease, and the relevance of acceleration curves and train excitation becomes less obvious; the intersections of moving load speed-lines and subsoil dispersion curves are some resonance frequencies that cause the amplification of ground vibrations; there exists a critical speed for moving train that is close to the minimum velocity of the Rayleigh's wave in the subsoil.     

Simulation of track-ground vibrations due to a high-speed train: the case of X-2000 at Ledsgard

This paper attempts to demonstrate an application of the author's simulation model for predicting the train-track and nearby ground-borne vibrations by the Swedish high-speed train X-2000 at Ledsgard. The validation of the computation results are tested against the available field measurement data at the site. In this way, the theoretical prediction of the model can be verified whilst also providing a clear-cut explanation of the observed data. The findings are stated as follows:The train-induced vibrations at the track differ significantly depending on train geometry and speed. At low speeds the response is quasi-static so that the track response due to train axle loads appears mostly downward at the point of their action. On the other hand, at high speeds the train-induced response becomes dynamic due to the inertia generated in the track-ground system, so that the track vibrations appear evenly in both upward and downward directions. As the results of the soft soil deposits at Ledsgard, the high train speed is almost in the trans-Rayleigh wave state so that a large amplified track response appeared due to the resonance between the track behavior and the Rayleigh wave propagation in the ground. This is explained by the frequency-wavenumber spectrum.To provide useful engineering information relating to vibration mitigation at the train track and nearby ground, a preliminary investigation was carried out by simulating the effect of constructing of a wave impeding barrier (WIB) at the site. The aforementioned frequency-wavenumber spectrum showed that the stiffening effects by the WIB installation into soft layers led a shift of response from a large dynamic one at high train speeds to a small, quasi-static one.     

The experimental validation of a numerical model for the prediction of the vibrations in the free field produced by road traffic

The objective of the present paper is the experimental validation of a numerical model for the prediction of traffic-induced vibrations. The vibrations in the free field, generated by the passage of a vehicle on an uneven road, are predicted in two stages. First, the equations of motion of the vehicle are solved to determine the dynamic axle loads. Next, these axle loads are applied to the road and the free field vibrations are computed. An elaborate measurement campaign has been set up to validate this model. The response of a Volvo FL6 truck and the response in the free field have been measured simultaneously during the passage of the truck over an artificial road unevenness. The parameters related to the vehicle, the road and the soil have been determined experimentally. A comparison of the predicted and the measured response demonstrates the predictive qualities of the numerical model. Furthermore, the results provide a clear insight in the influence of the vehicle speed on the vehicle's and the free field response.     

Sounds and vibrations in the frozen Beaufort Sea during gravel island construction

Underwater and airborne sounds and ice-borne vibrations were recorded from sea-ice near an artificial gravel island during its initial construction in the Beaufort Sea near Prudhoe Bay, Alaska. Such measurements are needed for characterizing the properties of island construction sounds to assess their possible impacts on wildlife. Recordings were made in February-May 2000 when BP Exploration (Alaska) began constructing Northstar Island about 5 km offshore, at 12 m depth. Activities recorded included ice augering, pumping sea water to flood the ice and build an ice road, a bulldozer plowing snow, a Ditchwitch cutting ice, trucks hauling gravel over an ice road to the island site, a backhoe trenching the sea bottom for a pipeline, and both vibratory and impact sheet pile driving. For all but one sound source (underwater measurements of pumping) the strongest one-third octave band was under 300 Hz. Vibratory and impact pile driving created the strongest sounds. Received levels of sound and vibration, as measured in the strongest one-third octave band for different construction activities, reached median background levels <7.5 km away for underwater sounds, <3 km away for airborne sounds, and <10 km away for in-ice vibrations.     

Modelling of continuous and discontinuous floating slab tracks in a tunnel using a periodic approach

This paper presents a periodic approach to couple a track and a tunnel-soil system of different periodicity. The periodicity of the track and the tunnel-soil system is exploited using the Floquet transform to efficiently formulate the problem in the frequency-wavenumber domain as well as to limit the discretization effort to a reference cell. The track and the tunnel-soil system are modelled as two separate systems of different periodicity and are coupled in the frequency-wavenumber domain. A coupled periodic finite element-boundary element method is used to model the tunnel-soil system, while a periodic finite element model or an analytical approach is used to model the track.A general analytical formulation to compute the response of three-dimensional periodic media that are excited by moving loads is discussed. It is shown that the response due to moving loads on the track can be calculated from the transfer function of the track-tunnel-soil system and the axle loads.A methodology for computing the transfer functions of the coupled track-tunnel-soil system as well as the computation of dynamic forces accounting for the interaction between the moving vehicle and the periodic track are described. The model accounts for quasi-static forces as well as dynamic forces due to parametric excitation and unevenness excitation.The methodology has been used to assess the vibration isolation efficiency of continuous and discontinuous floating slab tracks. It is concluded that both continuous and discontinuous floating slab tracks have a similar efficiency in the frequency range well above the isolation frequency of the slabs, which is usually higher than the slab passage frequency. In case of discontinuous slab tracks, the parametric excitation is found to be important, which results in a poorer performance of the track at low frequencies.     

Propagation of ground vibrations near railway tracks

Measurements of vibration propagation have been carried out at three different sites with different ground properties. Accelerometers were placed at distances up to 64 m from the center line of railroad tracks. The signals have been analyzed in one-third octave bands from 6·3 to 160 Hz. The results are rather independent of the sites investigated. Local differences in vibration level observed at one site are similar to level differences from site to site. For the prediction of train induced vibrations in the vicinity of planned railroad tracks, a simple power law is proposed.     

The influence of source–receiver interaction on the numerical prediction of railway induced vibrations

The numerical prediction of vibrations in buildings due to railway traffic is a complicated problem where wave propagation in the soil couples the source (railway tunnel or track) and the receiver (building). This through–soil coupling is often neglected in state-of-the-art numerical models in order to reduce the computational cost. In this paper, the effect of this simplifying assumption on the accuracy of numerical predictions is investigated. A coupled finite element–boundary element methodology is employed to analyze the interaction between a building and a railway tunnel at depth or a ballasted track at the surface of a homogeneous halfspace, respectively. Three different soil types are considered. It is demonstrated that the dynamic axle loads can be calculated with reasonable accuracy using an uncoupled strategy in which through–soil coupling is disregarded. If the transfer functions from source to receiver are considered, however, large local variations in terms of vibration insertion gain are induced by source–receiver interaction, reaching up to 10 dB and higher, although the overall wave field is only moderately affected. A global quantification of the significance of through–soil coupling is made, based on the mean vibrational energy entering a building. This approach allows assessing the common assumption in seismic engineering that source–receiver interaction can be neglected if the distance between source and receiver is sufficiently large compared to the wavelength of waves in the soil. It is observed that the interaction between a source at depth and a receiver mainly affects the power flow distribution if the distance between source and receiver is smaller than the dilatational wavelength in the soil. Interaction effects for a railway track at grade are observed if the source–receiver distance is smaller than six Rayleigh wavelengths. A similar trend is revealed if the passage of a freight train is considered. The overall influence of dynamic through–soil coupling in terms of power flow remains limited to 2 dB, but the insertion gain at particular locations can easily reach 10 dB. This is of the same order of magnitude as other sources of uncertainty in the numerical prediction of railway induced vibrations; this should hence be accounted for when performing vibration predictions.     

On rail vehicle vibrations induced by track unevenness: Analysis of the excitation mechanism

This paper deals with the analysis of the vibrations induced on the carbody of a rail vehicle by track unevenness. Attention is focused on the excitation mechanism of the carbody vibration modes, which has a strong influence on the vehicle's comfort. At first the problem is investigated through a simple three-degree-of-freedom analytical model, and the phenomenon of the critical velocities is analysed, pointing out how both rigid and flexible carbody vibration modes can be excited to a different extent, depending on the vehicle speed, and how they combine to produce the final carbody accelerations. Then the dynamic response of a real vehicle running on irregular track is simulated through a more detailed multibody model, suitable for quantitatively reproducing its dynamic behaviour in the 0-25 Hz frequency range. The 68 degrees-of-freedom of this model correspond to 35 rigid vibration modes of the vehicle components (carbody, bogie frames and wheelsets), plus the 33 carbody flexible modes which fall into the frequency-range of interest. In the last part of the paper, the obtained numerical results are compared to the experimental data collected during on-line tests, showing how the adopted numerical model accurately simulates the dynamic behaviour of the real vehicle at the different velocities, with very good agreement. The results presented in the paper demonstrate that the excitation of the flexible modes may have a decisive effect on carbody accelerations and that introducing carbody flexibility in the vehicle model turns out to be unavoidable for properly predicting a rail vehicle comfort performance.     

A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft

This paper describes a hybrid technique that combines Statistical Energy Analysis (SEA) predictions for structural vibration with acoustic modal summation techniques to predict interior noise levels in rotorcraft. The method was applied for predicting the sound field inside a mock-up of the interior panel system of the Sikorsky S-92 helicopter. The vibration amplitudes of the frame and panel systems were predicted using a detailed SEA model and these were used as inputs to the model of the interior acoustic space. The spatial distribution of the vibration field on individual panels, and their coupling to the acoustic space were modeled using stochastic techniques. Leakage and nonresonant transmission components were accounted for using space-averaged values obtained from a SEA model of the complete structural-acoustic system. Since the cabin geometry was quite simple, the modeling of the interior acoustic space was performed using a standard modal summation technique. Sound pressure levels predicted by this approach at specific microphone locations were compared with measured data. Agreement within 3 dB in one-third octave bands above 40 Hz was observed. A large discrepancy in the one-third octave band in which the first acoustic mode is resonant (31.5 Hz) was observed. Reasons for such a discrepancy are discussed in the paper. The developed technique provides a method for modeling helicopter cabin interior noise in the frequency mid-range where neither FEA nor SEA is individually effective or accurate.     

The cepstrum: a viable method for the removal of ground reflections

Noise data from open air test facilities is contaminated by the effect of ground reflections causing cancellations and augmentations of the sound at certain frequencies. This problem is generally dealt with by placing microphones near the ground and subtracting 6 dB from the SPL spectrum. However the high frequency part of the spectrum obtained in this way suffers from problems due to temperature gradients near the ground on sunny days. The present empirical method used at Rolls-Royce for the estimation of one third octave band free field spectra involves the use of two microphones, one at 0·051 m above the ground (ground level) for frequencies up to 1 kHz and the other at 1·524 m above the ground for higher frequencies. Corrections are applied to the one third octave spectra from these low and high microphones to take account of intensity increases. These spectra are then “married” at 1 kHz to produce a single free field spectrum. At present there is no similar method to obtain narrow band free field spectra. In this paper cepstrum analysis is proposed as a satisfactory method to produce both narrow band and one third octave band free field spectra from high level microphones only. A series of tests has been carried out in an anechoic chamber facility in which ground reflections were simulated. The cepstrum technique was applied to this data to deduce the free field spectra. These compared very well with free field spectra obtained under anechoic conditions. Data is also included from open air tests on the Viper 11 engine and the spinning rig jet noise facility to show that the cepstrum technique is a viable way of removing ground reflections from high level microphone data.     

Evaluation of track stiffness and track damping

Correct estimation of track stiffness and track damping is essential for predicting the dynamic wheel loads of railway vehicles running on rough tracks. While several analytical procedures have been developed in the past to estimate track stiffness, there is no procedure readily available for estimating track damping. Experimental techniques involving the use of impulse tests have been used in this study to estimate track stiffness and track damping, on several different track structures on the Indian Railways. The results of these tests are presented.     

On the dynamic response at the wheel axle of a pneumatic tire

A method for calculating the steady state displacement response and force transmission at the wheel axle of a pneumatic tire-suspension system due to a steady state force or displacement excitation at the tire to ground contact point is developed. The method requires the frequency responses (or receptances)_of both tire-wheel and suspension units. The frequency response of the tire-wheel unit is obtained by using the modal expansion method. The natural frequencies and mode shapes of the tire-wheel unit are obtained by using a geometrically non-linear, ring type, thin shell finite element of laminate composite. The frequency response of the suspension unit is obtained analytically. These frequency responses are used to calculate the force-input and the displacement-input responses at the wheel axle. This method allows the freedom of designing a vehicle and its tires independently and still achieving optimum dynamic performance.     

Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core

In this study, magneto-rheological elastomers (MREs) are adopted to construct a smart sandwich beam for micro-vibration control of equipment. The micro-vibration response of a smart sandwich beam with MRE core which supports mass-concentrated equipment under stochastic support-motion excitations is investigated to evaluate the vibration suppression capability. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of the smart sandwich beam supporting mass-concentrated equipment is developed based on the Galerkin method and random vibration theory. First, the displacements of the beam are expanded as series of spatial harmonic functions and the Galerkin method is applied to convert the partial differential equations of motion into ordinary differential equations. With these equations, the frequency-response function matrix of the beam–mass system and the expression of the velocity response spectrum are then obtained, with which the root-mean-square (rms) velocity response in terms of the one-third octave frequency band can be calculated. Finally, the optimization problem of the complex modulus of the MRE core is defined by minimizing the velocity response spectrum and the rms velocity response of the sandwich beam, through altering the applied magnetic fields. Numerical results are given to illustrate the influence of MRE parameters on the rms velocity response and the response reduction capacity of the smart sandwich beam. The proposed method is also applicable to response analysis of a sandwich beam with arbitrary core characterized by a complex shear modulus and subject to arbitrary stochastic excitations described by a power spectral density function, and is valid for a wide frequency range.     

Forced transverse vibrations of an elastically connected complex simply supported double-beam system

The present paper is devoted to analyzing undamped forced transverse vibrations of an elastically connected complex double-beam system. The problem is formulated and solved in the case of simply supported beams. The classical modal expansion method is applied to ascertain dynamic responses of beams due to arbitrarily distributed continuous loads. Several cases of particularly interesting excitation loadings are investigated. The action of stationary harmonic loads and moving forces is considered. In discussing vibrations caused by exciting harmonic forces, conditions of resonance and dynamic vibration absorption are determined. The beam-type dynamic absorber is a new concept of a continuous dynamic vibration absorber (CDVA), which can be applied to suppress excessive vibrations of corresponding beam systems. A numerical example is presented to illustrate the theoretical analysis.     

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

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

Piston scuffing fault and its identification in an IC engine by vibration analysis

In this paper, the effects of piston scuffing fault on engine performance and vibrations are investigated. A procedure based on vibration analysis is also presented to identify piston scuffing fault. To this end, an internal combustion (IC) engine ran under a specific test procedure. The engine parameters and vibration signals were measured during the experiments. To produce piston scuffing fault, three-body abrasive wear mechanism was employed. The experimental results showed that piston scuffing fault caused the engine performance to reduce significantly. The vibration signals were analyzed in time-domain, frequency-domain and time–frequency domain. Continuous wavelet transform (CWT) was used to obtain time–frequency representations. “dmey” wavelet was selected as the optimum wavelet type for this research among different wavelet types using the three criteria of energy, Shannon entropy and energy to Shannon entropy ratio. The results of CWT analysis by “dmey” wavelet showed that piston scuffing fault excited the frequency band of 2.4–4.7 kHz in which the frequency of 3.7 kHz was affected more. Finally, seven different features were extracted from the engine vibration signals related to the frequency band of 2.4–4.7 kHz. The results indicated that maximum, mean, RMS, skewness, kurtosis and impulse factor of the engine vibration related to the found frequency band increased significantly due to piston scuffing fault. The obtained results showed that the proposed method identified piston scuffing fault and discovered the vibration characteristics of this fault like frequency band. The results also demonstrated the possibility of using engine vibrations in piston scuffing fault identification.     

Effects of signal processing on the measurement of maximum sound pressure levels

Maximum sound pressure levels are commonly used for environmental noise and building acoustics measurements. This paper investigates the signal processing errors due to Fast or Slow time-weighting detectors when combined with octave band filters, one-third octave band filters or an A-weighting filter. For 6th order Butterworth CPB filters the inherent time delay caused by the phase response of filters is quantified using three different approaches to establish the following rules-of-thumb: (1) time-to-gradient/amplitude matching occurs when Bt ≈ 1, (2) time-to-peak matching occurs when Bt ≈ 2 and (3) time-to-settle matching occurs when Bt ≈ 4 for octave band filters, and when Bt ≈ 3 for one-third octave band filters. Four different commercially-available sound level meters are used to quantify the variation in measured maximum levels using tone bursts, half-sine pulses, ramped noise and recorded transients. Tone bursts indicate that Slow time-weighting is inappropriate for maximum level measurements due to the large bias error. The results also show that there is more variation between sound level meters when considering Fast time-weighted maximum levels in octave bands or one-third octave bands than with A-weighted levels. To reduce the variation between measurements with different sound level meters, it is proposed that limits could be prescribed on the phase response for CPB filters and A-weighting filters.     

Verification of an empirical prediction method for railway induced vibrations by means of numerical simulations

Vibrations induced by the passage of trains are a major environmental concern in urban areas. In practice, vibrations are often predicted using empirical methods such as the detailed vibration assessment procedure of the Federal Railroad Administration (FRA) of the U.S. Department of Transportation. This procedure allows predicting ground surface vibrations and re-radiated noise in buildings. Ground vibrations are calculated based on force densities, measured when a vehicle is running over a track, and line source transfer mobilities, measured on site to account for the effect of the local geology on wave propagation. Compared to parametric models, the advantage of this approach is that it inherently takes into account all important parameters. It can only be used, however, when an appropriate estimation of the force density is available. In this paper, analytical expressions are derived for the force density and the line source transfer mobility of the FRA procedure. The derivation of these expressions is verified using a coupled finite element-boundary element method.     

Ground vibrations from passing trains

As railway operating practice has evolved, so trains have become faster and also in the case of freight trains heavier, with increased axle loads. To carry this traffic, heavier track has been introduced and maintenance programmes intensified. This paper examines the residual problems of ground-borne vibration, the vehicle and track features which might be responsible for generation, how it is propagated, and how it might affect wayside buildings. Experimental work has suggested various significant features of railway design which might merit attention.