phase_velocity.py - A Python algorithm for calculating frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars
The correlation between normalised frequency and phase velocity, m1 and m2, can be utilised to account for first-mode dispersion effect in pressure bar measurements using process_SHPB.py (see Van Lerberghe and Barr (2023)).
The open-source python algorithm phase_velocity.py, finds the first root of Bancroft’s (1941) equation using the bisection method, for a defined Poisson’s ratio, and over a defined range of normalised wavelength (d/L). The result is the normalised wave velocity, cp/c0, which corresponds to the first mode of propagation for longitudinal waves in an elastic cylindrical bar. Normalised wavelengths are also converted to normalised frequencies, fa/c0.
Normalised phase velocities are then used to calculate Tyas and Wilson’s (2001) factors m1 and m2, which account for wavelength dependent radial fluctuations in strain and Young’s modulus respectively.
The results m1, m2, norm_freqs and v_ratios are saved in 4 separate pickle files, in a folder titled dispersion-factors, for the corresponding Poisson’s ratio selected.
Both process_SHPB.py and phase_velocity.py, open-source Python algorithms on GitHub and ORDA, with their respective links attached below. They are inspired by Matlab scripts created by Barr (2016 & 2023), see below.
- phase_velocity.py: Includes the main python function phase_velocity.py, with the documentation on the use of the function included in the file as comments.
- phase_velocity.pdf: An image showing the phase velocities, the factor m1 and normalised factor m2/E.
- Bancroft, D. (1941) The Velocity of Longitudinal Waves in Cylindrical Bars. Physical Review, 59, 588-593.
- Tyas, A., Wilson, A. J. (2001) An investigation of frequency domain dispersion correction of pressure bar signals. International Journal of Impact Engineering, 25, 87-101.
- Barr, A. D. (2016) dispersion.m - A Matlab script for phase angle and amplitude correction of pressure bar signals. University of Sheffield.
Software ORDA link: [https://doi.org/10.15131/shef.data.3996876.v1]
- Barr, A. D. (2023) phasevelocity.m - A Matlab script to calculate the frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars. University of Sheffield.
Software ORDA link: [https://doi.org/10.15131/shef.data.21982604.v1]
- Van Lerberghe, A., Barr, A. D. (2023) process_SHPB.py- a Python algorithm for stress wave dispersion correction in split-Hopkinson pressure bar experiments. University of Sheffield.
Software ORDA link: [https://doi.org/10.15131/shef.data.21973325]
Software GitHub link: [https://github.com/ArthurVL-maker/Process_SHPB.git]
- Van Lerberghe, A., Barr, A. D. (2023) phase_velocity.py - A Python algorithm for calculating frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars. University of Sheffield.
Software GitHub link: [https://github.com/ArthurVL-maker/Phase_velocity.git]
- There is no personal data or any that requires ethical approval
- The data complies with the institution and funders' policies on access and sharing
Sharing and access restrictions
- The data can be shared openly
- The file formats are open or commonly used
Methodology, headings and units
- There is a file including methodology, headings and units, such as a readme.txt