ModalStressProportions.xlsx (17.19 kB)

Data for the proportion of longitudinal stress travelling in Modes 1-4 in a Hopkinson pressure bar, for 0.35 < fa/c0 < 0.90, at the bar surface and as a cross-sectional mean

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posted on 26.01.2020 by Andrew Barr, Samuel Rigby, Max Clayton
This dataset contains tabulated values for how the stress in a high frequency waveform will be divided between each of the first four propagating modes, for longitudinal waves in cylindrical pressure bars, up to a normalised frequency of fa/c0=0.9. This data can be used to perform four-mode dispersion correction of high frequency signals, such as overpressure measurements from blast loading using Hopkinson pressure bars.

Data was calculated using LS-DYNA to model the propagation of single-frequency pulses in a long steel pressure bar. At each normalised frequency a short, raised-cosine windowed sinusoidal forcing function was applied to the end of the bar. The stress in the bar dispersed into multiple modal 'pulses' as it propagated, allowing the contribution of each mode to be calculated from the amplitude of the pulses.

Values are provided up to a normalised frequency of fa/c0 = 0.9, where f is frequency, a is the radius of the bar, and c0 is the one-dimensional wave speed. The table indicates whether the values are modelled directly in LS-DYNA (M) or calculated by interpolation of the modelled results (I).

More details are available in our Impact Engineering paper below:

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