Investigation of acoustic transmission beneath a railway vehicle by using statistical energy analysis and an equivalent source model

Abstract

An approach is presented for modelling the noise propagation beneath the train floor and this is applied to rolling noise sources. It is assumed that the sound incident on the train floor is made up of a direct and a reverberant component. A combination of two numerical modelling approaches is considered to deal with these: an equivalent source model, to represent the direct component, and statistical energy analysis (SEA) for the reverberant part. In the equivalent source model, the wheel is replaced by monopole and dipole sources, which represent its radial and axial radiation. The rail vertical vibration and the sleepers are replaced by arrays of monopole sources while the rail lateral vibration is replaced by an array of lateral dipoles. The sound power of the rolling noise is obtained by using the TWINS model. In the SEA model, the region beneath the train floor is divided into several volumes and the power input to these subsystems is assumed to be due to the first reflections from the train floor and the ground. The reverberant and direct sound have very similar contributions to the total sound power incident on the train floor although this depends on how the equipment is arranged beneath the train. The modelling approach is verified by comparing the predicted sound pressure levels with laboratory measurements and with field tests.

A framework to predict the airborne noise inside railway vehicles with application to rolling noise

“…The input power is calculated by multiplying the sound power incident on the train floor and sidewalls by their corresponding transmission coefficients. These incident sound powers are calculated using different methods [30,31]. They are summarised in Section 3.1 and Section 3.2.…”

“…In this environment the total sound power incident on the train floor (𝑊 f ) can be expressed as the sum of a direct (𝑊 dir ) and a reverberant (𝑊 rev ) component [32] 𝑊 f = 𝑊 dir + 𝑊 rev (5) The direct sound can be calculated by modelling the wheel, the rail and the sleepers as equivalent point sources [30,33]. For the wheels, a point source Sq is located at the geometrical centre of the wheel [30]. The radial and axial radiation of the wheel are modelled by a monopole and a lateral dipole respectively according to their directivity [3].…”

“…where p is the sound pressure incident on the train floor and 𝑢 𝑧 * is the conjugate of the corresponding velocity normal to the train floor [30].…”

“…Details of the SEA model below the vehicle are elaborated in Ref. [30]. The space beneath the vehicle is subdivided into several segments, as illustrated in Figure 2.…”

“…After the direct and reverberant sound power being calculated, they are adjusted by the source strengths of rolling noise obtained from the TWINS model [35], which is presented in [30].…”