A numerical investigation of dispersion in Hopkinson Pressure Bar experiments

Abstract
The majority of published research on numerical modelling of Split Hopkinson Pressure Bars (SHPB) focuses on the response of the specimen, with very little attention given to the dispersive wave propagation in the bars themselves. This investigation focussed on the numerical modelling of wave propagation in cylindrical pressure bars. The Eigen modes of an infinitely long cylindrical bar were compared to the vibrational modes predicted by the analytical solution of Pochammer and Chree. There was very good agreement between the numerical and analytical predictions for the phase velocity-frequency relationship derived from the Eigen modes. Eigen analysis of a finite length bar showed several differences. The most notable of these was that the infinite bar Eigen modes could be characterised by a single wavelength whereas most finite bar Eigen modes required two or more wavelengths. The response of a finite bar to an evenly distributed oscillating pressure pulse was modelled using Abaqus/Explicit. The numerical predictions compared well with the analytical predictions, for frequencies below 100 kHz, but large discrepancies arose at higher frequencies.