Modelling of vibration and noise behaviour of embedded tram tracks using a wavenumber domain method

Abstract

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