A 2.5D acoustic finite element method applied to railway acoustics

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