READ ME File For 'Data supporting the article: An efficient model for predicting the sound radiation from a railway rail accounting for cross-section deformation' Dataset DOI: https://doi.org/10.5258/SOTON/D3586 Date that the file was created: July, 2025 ------------------- GENERAL INFORMATION ------------------- ReadMe Author: Christopher Knuth, University of Southampton -------------------------- SHARING/ACCESS INFORMATION -------------------------- Licenses/restrictions placed on the data, or limitations of reuse: CC BY Recommended citation for the data: This dataset supports the publication: AUTHORS: Christopher Knuth, Giacomo Squicciarini, David Thompson TITLE: An efficient model for predicting the sound radiation from a railway rail accounting for cross-section deformation JOURNAL: Journal of Sound and Vibration PAPER DOI: https://doi.org/10.1016/j.jsv.2025.119323 -------------------- DATA & FILE OVERVIEW -------------------- This dataset contains the numerical data used to produce Figures 5-23 of the publication, some of which are divided into sub-figures from (a)-(c). -It is separated into 31 Microsoft Excel files (.xls), one for each sub-figure. -The x- and y-data are stored as columns in the sheet and if all y-data are the same length, the first column corresponds to the x-data and the remaining ones to the y-data of each line (except from Figure_16a.xls and Figure_16b.xls, where z-data is also stored as they are 2D surface plots where x-/y-data are ordered in rows/columns) -A description is available in each sheet, that refers the data to the corresponding line in the (sub-)figure. In the ZIP file the data is organised as follows: - Figure_5.xls - Figure_6.xls - Figure_7a.xls - Figure_7b.xls - Figure_8a.xls - Figure_8b.xls - Figure_9a.xls - Figure_9b.xls - Figure_11a.xls - Figure_11b.xls - Figure_12.xls - Figure_13.xls - Figure_14.xls - Figure_15a.xls - Figure_15b.xls - Figure_16a.xls - Figure_16b.xls - Figure_17a.xls - Figure_17b.xls - Figure_18a.xls - Figure_18b.xls - Figure_19a.xls - Figure_19b.xls - Figure_20a.xls - Figure_20b.xls - Figure_21a.xls - Figure_21b.xls - Figure_22.xls - Figure_23a.xls - Figure_23b.xls - Figure_23c.xls -------------------------- METHODOLOGICAL INFORMATION -------------------------- Description of methods used for collection/generation of data: The data was generated from numerical simulations in MATLAB Methods for processing the data: The simulations were carried out using the 2.5D FE/BE model of the supported track developed in this paper which is combined with a rotating wheelset model (published earlier by the authors, see DOI: 10.1016/j.jsv.2023.118180) in a rolling noise prediction scheme following the TWINS (Track-Wheel Interaction Noise Software) procedure. -------------------------- DATA-SPECIFIC INFORMATION -------------------------- Figure_5.xls: Interpolation of the Hankel function (real part) column 1 - x-data: alpha*r (continuous) in [rad] column 2 - y-data: Hankel function exact in [-] column 3-5 - y-data: Hankel function interpolated linear,quadratic,quartic in [-] column 6 - x-data: alpha*r (discrete) in [rad] column 7 - y-data: Hankel function discrete in [-] Figure_6.xls: Error in the 2.5D BE interpolation method compared to conventional 2.5D BE column 1 - x-data: number of alpha_i points in [-] column 2-4 - y-data: error linear,quadratic,quartic interpolation in [dB] Figure_7a.xls: Comparison between measured and simulated driving point mobility for vertical excitation column 1 - x-data: frequency in [Hz] column 2-3 - y-data: simulated mobility magnitude in [m/(NS)] and phase in [rad] column 4-5 - y-data: measured mobility magnitude in [m/(NS)] and phase in [rad] Figure_7b.xls: Comparison between measured and simulated driving point mobility for lateral excitation column 1 - x-data: frequency in [Hz] column 2-3 - y-data: simulated mobility magnitude in [m/(NS)] and phase in [rad] column 4-5 - y-data: measured mobility magnitude in [m/(NS)] and phase in [rad] Figure_8a.xls: Comparison between measured and simulated track decay rate for vertical excitation column 1 - x-data: frequency in [Hz] column 2 - y-data: simulated track decay rate in [dB/m] column 3 - y-data: measured track decay rate in [dB/m] Figure_8b.xls: Comparison between measured and simulated track decay rate for lateral excitation column 1 - x-data: frequency in [Hz] column 2 - y-data: simulated track decay rate in [dB/m] column 3 - y-data: measured track decay rate in [dB/m] Figure_9a.xls: Real part of wavenumbers of the symmetric waves from the Timoshenko beam and 2.5D FE models column 1 - x-data: frequency in [Hz] column 2 - y-data: wavenumber in air [rad/m] column 3-4 - y-data: wavenumbers (bending+shear) in Timoshenko beam [rad/m] column 5-10 - y-data: wavenumbers in 2.5D FE [rad/m] Figure_9b.xls: Real part of wavenumbers of the antisymmetric waves from the Timoshenko beam and 2.5D FE models column 1 - x-data: frequency in [Hz] column 2 - y-data: wavenumber in air [rad/m] column 3 - y-data: wavenumber (bending only) in Timoshenko beam [rad/m] column 4-8 - y-data: wavenumbers in 2.5D FE [rad/m] Figure_11a.xls: Imaginary part of wavenumbers of the symmetric waves as decay rate from the Timoshenko beam and 2.5D FE models column 1 - x-data: frequency in [Hz] column 2-3 - y-data: wavenumbers in Timoshenko beam [rad/m] column 4-9 - y-data: wavenumbers in 2.5D FE [rad/m] Figure_11b.xls: Imaginary part of wavenumbers of the antisymmetric waves as decay rate from the Timoshenko beam and 2.5D FE models column 1 - x-data: frequency in [Hz] column 2-3 - y-data: wavenumbers in Timoshenko beam [rad/m] column 4-9 - y-data: wavenumbers in 2.5D FE [rad/m] Figure_12.xls: Vertical driving point mobility comparing the Timoshenko beam and 2.5D FE rail vibration at the rail head centre at x=0 column 1 - x-data: frequency in [Hz] column 2-3 - y-data: Timoshenko beam mobility magnitude in [m/(Ns)] and phase in [rad] column 4-5 - y-data: 2.5D FE mobility (sum all waves) magnitude in [m/(Ns)] and phase in [rad] column 6-11 - y-data: 2.5D FE mobility (individual propagating waves) magnitude in [m/(Ns)] Figure_13.xls: Vertical transfer point mobility comparing the Timoshenko beam and 2.5D FE rail vibration at the rail foot for excitation at the rail head centre at x=0 column 1 - x-data: frequency in [Hz] column 2-3 - y-data: Timoshenko beam mobility magnitude in [m/(Ns)] and phase in [rad] column 4-5 - y-data: 2.5D FE mobility (sum all waves) magnitude in [m/(Ns)] and phase in [rad] column 6-11 - y-data: 2.5D FE mobility (individual propagating waves) magnitude in [m/(Ns)] Figure_14.xls: Lateral driving point mobility comparing the Timoshenko beam and 2.5D FE rail vibration at the rail head centre at x=0 column 1 - x-data: frequency in [Hz] column 2-3 - y-data: Timoshenko beam mobility magnitude in [m/(Ns)] and phase in [rad] column 4-5 - y-data: 2.5D FE mobility (sum all waves) magnitude in [m/(Ns)] and phase in [rad] column 6-10 - y-data: 2.5D FE mobility (individual propagating waves) magnitude in [m/(Ns)] Figure_15a.xls: Vertical transfer mobility comparing the Timoshenko beam and 2.5D FE rail models at the rail head centre over distance x at a frequency of 1000 Hz column 1 - x-data: distance in [m] column 2 - y-data: Timoshenko beam (original) mobility magnitude in [m/(Ns)] column 3 - y-data: Timoshenko beam (corrected) mobility magnitude in [m/(Ns)] column 4 - y-data: 2.5D FE mobility (all waves) magnitude in [m/(Ns)] column 5-9 - y-data: 2.5D FE mobility (individual propagating waves) magnitude in [m/(Ns)] Figure_15b.xls: Vertical transfer mobility comparing the Timoshenko beam and 2.5D FE rail models at the rail head centre over distance x at a frequency of 5100 Hz column 1 - x-data: distance in [m] column 2 - y-data: Timoshenko beam (original) mobility magnitude in [m/(Ns)] column 3 - y-data: Timoshenko beam (corrected) mobility magnitude in [m/(Ns)] column 4 - y-data: 2.5D FE mobility (all waves) magnitude in [m/(Ns)] column 5-9 - y-data: 2.5D FE mobility (individual propagating waves) magnitude in [m/(Ns)] Figure_16a.xls: Sound power level of 2.5D FE in frequency and wavenumber domain (2D plot) for vertical excitation at rail head centre with unit squared force row 3 - x-data: frequency in [Hz] column 2 - y-data: wavenumber in [rad/m] row 3-end/column 2-end - z-data: sound power level of 2.5D FE in [dB re 1e-12 W/(mN^2)] Figure_16b.xls: Sound power level of 2.5D FE in frequency and wavenumber domain (2D plot) for lateral excitation at rail head centre with unit squared force row 3 - x-data: frequency in [Hz] column 2 - y-data: wavenumber in [rad/m] row 3-end/column 2-end - z-data: sound power level of 2.5D FE in [dB re 1e-12 W/(mN^2)] Figure_17a.xls: Sound power level comparing the Timoshenko beam and 2.5D FE rail models for vertical excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level Timoshenko beam (original) in [dB re 1e-12 W/N^2] column 3 - y-data: sound power level Timoshenko beam (corrected) in [dB re 1e-12 W/N^2] column 4 - y-data: sound power level 2.5D FE in [dB re 1e-12 W/N^2] Figure_17b.xls: Sound power level difference between the Timoshenko beam and 2.5D FE rail models for vertical excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference of Timoshenko beam (original) in [dB] column 3 - y-data: sound power level difference of Timoshenko beam (corrected) in [dB] Figure_18a.xls: Sound power level comparing the Timoshenko beam and 2.5D FE rail models for lateral excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level Timoshenko beam (original) in [dB re 1e-12 W/N^2] column 3 - y-data: sound power level 2.5D FE in [dB re 1e-12 W/N^2] Figure_18b.xls: Sound power level difference between the Timoshenko beam and 2.5D FE rail models for lateral excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference of Timoshenko beam (original) in [dB] Figure_19a.xls: Spatially averaged velocity level comparing the Timoshenko beam and 2.5D FE rail models for vertical excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: velocity level Timoshenko beam (original) in [dB re 1 m^3/(N^2s^2)] column 3 - y-data: velocity level Timoshenko beam (corrected) in [dB re 1 m^3/(N^2s^2)] column 4 - y-data: velocity level 2.5D FE in [dB re 1 m^3/(N^2s^2)] Figure_19b.xls: Spatially averaged velocity level comparing the Timoshenko beam and 2.5D FE rail models for lateral excitation at the rail head centre with unit squared force column 1 - x-data: frequency in [Hz] column 2 - y-data: velocity level Timoshenko beam (original) in [dB re 1 m^3/(N^2s^2)] column 3 - y-data: velocity level 2.5D FE in [dB re 1 m^3/(N^2s^2)] Figure_20a.xls: Radiation efficiency comparing the Timoshenko beam and 2.5D FE rail models for vertical excitation at the rail head centre column 1 - x-data: frequency in [Hz] column 2 - y-data: radiation ratio Timoshenko beam (original) in [dB re 1] column 3 - y-data: radiation ratio 2.5D FE in [dB re 1] Figure_20b.xls: Radiation efficiency comparing the Timoshenko beam and 2.5D FE rail models for lateral excitation at the rail head centre column 1 - x-data: frequency in [Hz] column 2 - y-data: radiation ratio Timoshenko beam (original) in [dB re 1] column 3 - y-data: radiation ratio 2.5D FE in [dB re 1] Figure_21a.xls: Rail sound power level in rolling noise calculation (TSI roughness) using Timoshenko beam and 2.5D FE rail models column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level Timoshenko beam (original) in [dB re 1e-12 W] column 3 - y-data: sound power level Timoshenko beam (corrected) in [dB re 1e-12 W] column 4 - y-data: sound power level 2.5D FE in [dB re 1e-12 W] Figure_21b.xls: Rail sound power level difference in rolling noise calculation (TSI roughness) between Timoshenko beam and 2.5D FE rail models column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference Timoshenko beam (original) in [dB] column 3 - y-data: sound power level difference Timoshenko beam (corrected) in [dB] Figure_22.xls: Driving point mobility at x=0 vertical/lateral cross-term of the 2.5D FE rail for excitation off-centre (1 cm shift from centre) compared with Timoshenko beam approximation column 1 - x-data: frequency in [Hz] column 2 - y-data: mobility of the 2.5D FE in [m/(Ns)] column 3 - y-data: mobility of the Timoshenko beam (with xdB=-8 dB) in [m/(Ns)] column 4 - y-data: mobility of the Timoshenko beam (with xdB=-10 dB) in [m/(Ns)] column 5 - y-data: mobility of the Timoshenko beam (with xdB=-12 dB) in [m/(Ns)] column 6 - y-data: mobility of the Timoshenko beam (with xdB=-14 dB) in [m/(Ns)] column 7 - y-data: mobility of the Timoshenko beam (with xdB=-16 dB) in [m/(Ns)] Figure_23a.xls: Rail sound power level difference (only component due to vertical force) in rolling noise calculation between the 2.5D FE rail with off-centre excitation (1 cm shift from centre) and Timoshenko beam approximations with and without vertical/lateral rail mobility cross-term column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference of Timoshenko beam (no mobility cross-term) in [dB] column 3 - y-data: sound power level difference of Timoshenko beam (with xdB=-8 dB) in [dB] column 4 - y-data: sound power level difference of Timoshenko beam (with xdB=-10 dB) in [dB] column 5 - y-data: sound power level difference of Timoshenko beam (with xdB=-12 dB) in [dB] column 6 - y-data: sound power level difference of Timoshenko beam (with xdB=-14 dB) in [dB] column 7 - y-data: sound power level difference of Timoshenko beam (with xdB=-16 dB) in [dB] Figure_23b.xls: Rail sound power level difference (only component due to lateral force) in rolling noise calculation between the 2.5D FE rail with off-centre excitation (1 cm shift from centre) and Timoshenko beam approximations with and without vertical/lateral rail mobility cross-term column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference of Timoshenko beam (no mobility cross-term) in [dB] column 3 - y-data: sound power level difference of Timoshenko beam (with xdB=-8 dB) in [dB] column 4 - y-data: sound power level difference of Timoshenko beam (with xdB=-10 dB) in [dB] column 5 - y-data: sound power level difference of Timoshenko beam (with xdB=-12 dB) in [dB] column 6 - y-data: sound power level difference of Timoshenko beam (with xdB=-14 dB) in [dB] column 7 - y-data: sound power level difference of Timoshenko beam (with xdB=-16 dB) in [dB] Figure_23c.xls: Rail sound power level difference in rolling noise calculation between the 2.5D FE rail with off-centre excitation (1 cm shift from centre) and Timoshenko beam approximations with and without vertical/lateral rail mobility cross-term column 1 - x-data: frequency in [Hz] column 2 - y-data: sound power level difference of Timoshenko beam (no mobility cross-term) in [dB] column 3 - y-data: sound power level difference of Timoshenko beam (with xdB=-8 dB) in [dB] column 4 - y-data: sound power level difference of Timoshenko beam (with xdB=-10 dB) in [dB] column 5 - y-data: sound power level difference of Timoshenko beam (with xdB=-12 dB) in [dB] column 6 - y-data: sound power level difference of Timoshenko beam (with xdB=-14 dB) in [dB] column 7 - y-data: sound power level difference of Timoshenko beam (with xdB=-16 dB) in [dB]