Abstract
The Hopkinson pressure bar is widely used to measure the reflected pressure of blast waves over a short distance. However, dispersion effects will occur when the elastic stress waves propagate in the pressure bar due to lateral inertia, and there will be errors between the signals obtained from the sensors and the actual loading. For the free surface velocity measured in our system, we developed a local phase-amplitude joint correction method to convert the measured velocity into the average reflected pressure of a shock wave at the impact end of the bar, considering factors such as propagation modes of the elastic wave, the frequency components’ time of arrival, velocity variation over the bar axis, and the stress–velocity relationship. Firstly, the Pochhammer–Chree frequency equation is calculated numerically, and the first to fourth orders of phase velocity, group velocity, normalized frequency, and propagation time curves of elastic wave propagation in 35CrMnSiA steel are obtained. Secondly, the phase and amplitude correction formulas for calculating average reflected pressure from center velocity are derived based on the propagation mode of the axial elastic wave in the pressure bar by analyzing the time-frequency combined spectrum obtained by short-time Fourier transform. Thirdly, a local phase-amplitude joint correction algorithm based on propagation mode is proposed in detail. The experimental tests and data analyses are carried out for eight sets of pressure bar. The results show that this method can identify the propagation mode of elastic waves in the bar intuitively and clearly. The first three orders of propagation modes are stimulated in the bar 04, while only the first order of propagation is stimulated in the other eight bars. The local phase-amplitude joint correction algorithm can avoid correcting the component of the non-axial elastic wave. The rising edge of the average stress curve on the impact surface of bar 01 and bar 04 is corrected from 4.13 μs and 4.09 μs to 2.70 μs, respectively.
Highlights
The Hopkinson pressure bar has been the primary means of recording expected high magnitude, short duration, initial loading for over one hundred years, since 1914 [1]
The main problem that has puzzled the measurement scientists is that the axial elastic stress wave is dispersed due to the lateral inertia effect, which leads to inconsistency between the signal obtained by the measuring element and the actual load on the front end of the pressure bar
For the free surface velocity measured in our system, we developed a local phase-amplitude joint correction method considering factors such as propagation mode of the elastic wave, frequency components’ time of arrival, velocity variation over the bar axis, and the stress–velocity relation
Summary
The Hopkinson pressure bar has been the primary means of recording expected high magnitude, short duration, initial loading for over one hundred years, since 1914 [1]. In 1978, Yew [11] used the fast Fourier transform method to analyze the strain signals at two measuring points on the pressure bar, and the phase velocity of each frequency component of the axial longitudinal wave obtained was consistent with the theoretical value of the first-order propagation mode of the P-C equation. These studies prove that the finite length pressure bar can still be studied based on P-C theory in practical applications. This method has the capability of identifying the propagation mode and correcting multi-mode dispersion except for the non-axial elastic wave
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