phase_velocity.py - A Python algorithm for calculating frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars

<h4>DESCRIPTION:</h4> <p>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 <em>process_SHPB.py</em> (see Van Lerberghe and Barr (2023)).</p> <p>The open-source python algorithm <em>phase_velocity.py</em>, 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.</p> <p>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.</p> <p>The results m1, m2, norm_freqs and v_ratios are saved in 4 separate pickle files, in a folder titled <em>dispersion-factors</em>, for the corresponding Poisson’s ratio selected.</p> <p>Both <em>process_SHPB.py</em> and <em>phase_velocity.py</em>, 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.</p> <h4>FILES INCLUDED:</h4> <ul> <li><em>phase_velocity.py</em>: Includes the main python function <em>phase_velocity.py</em>, with the documentation on the use of the function included in the file as comments.</li> <li><em>phase_velocity.pdf</em>: An image showing the phase velocities, the factor m1 and normalised factor m2/E.</li> </ul> <h4>REFERENCES:</h4> <ul> <li>Bancroft, D. (1941) The Velocity of Longitudinal Waves in Cylindrical Bars. Physical Review, 59, 588-593.</li> <li>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.</li> </ul> <h4>MATLAB SOFTWARE:</h4> <ul> <li>Barr, A. D. (2016) <em>dispersion.m</em> - A Matlab script for phase angle and amplitude correction of pressure bar signals. University of Sheffield.<br> Software ORDA link: [<a href="https://doi.org/10.15131/shef.data.3996876.v1" target="_blank">https://doi.org/10.15131/shef.data.3996876.v1</a>]</li> <li>Barr, A. D. (2023) <em>phasevelocity.m</em> - A Matlab script to calculate the frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars. University of Sheffield.<br> Software ORDA link: [<a href="https://doi.org/10.15131/shef.data.21982604.v1" target="_blank">https://doi.org/10.15131/shef.data.21982604.v1</a>]</li> </ul> <h4>PYTHON SOFTWARE:</h4> <ul> <li>Van Lerberghe, A., Barr, A. D. (2023) <em>process_SHPB.py</em>- a Python algorithm for stress wave dispersion correction in split-Hopkinson pressure bar experiments. University of Sheffield.<br> Software ORDA link: [<a href="https://doi.org/10.15131/shef.data.21973325" target="_blank">https://doi.org/10.15131/shef.data.21973325</a>]<br> Software GitHub link: [<a href="https://github.com/ArthurVL-maker/Process_SHPB.git" target="_blank">https://github.com/ArthurVL-maker/Process_SHPB.git</a>]</li> <li>Van Lerberghe, A., Barr, A. D. (2023) <em>phase_velocity.py</em> - A Python algorithm for calculating frequency-dependent phase velocity and radial variation of elastic waves in cylindrical bars. University of Sheffield.<br> Software GitHub link: [<a href="https://github.com/ArthurVL-maker/Phase_velocity.git" target="_blank">https://github.com/ArthurVL-maker/Phase_velocity.git</a>]</li> </ul> <h4>AUTHORS:</h4> <p>Arthur Van Lerberghe <a href="mailto:avanlerberghe1@sheffield.ac.uk" target="_blank">avanlerberghe1@sheffield.ac.uk</a> & Andrew D. Barr <a href="mailto:a.barr@sheffield.ac.uk" target="_blank">a.barr@sheffield.ac.uk</a>.</p>