Second Mode Vibrations of the Pochhammer-Chree Frequency Equation

Curtis, C. W.

doi:10.1063/1.1721775

Cited by 16 publications

(8 citation statements)

References 2 publications

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“…In the case of Oliver [19], a few phase velocities and group velocities were determined from the wave oscillations and compared with PC theory-predicted velocity versus period curves; qualitative consistency was observed. Curtis et al [20][21][22] interpreted the different types of oscillations to be caused by up to sixth-mode PC vibrations based on a qualitatively drawn frequency versus arrival time diagram. The qualitative consistencies of the wave velocities and arrival times in previous studies [18][19][20][21][22] essentially have limitations as a verification of the PC theory because the coincidence of the predicted wave profiles themselves with the experiment was unavailable.…”

Section: Usage and Verification Of The Combined Theoriesmentioning

confidence: 99%

“…Precise calibration of the one-dimensional (1D) sound speed (c o ) and Poisson's ratio (ν) of a circular bar is essential in using the split Hopkinson bar (SHB) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and Hopkinson bar (HB) [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In the case of SHB experiments, the specimen properties are generally determined using the following equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]:…”

Section: Introductionmentioning

confidence: 99%

“…2 Literature Survey 2.1 Dispersion Correction in Bar Technology. HB [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] has traditionally been used to measure a transient pulse generated by the impact of a near-field blast or bullets. Conversely, SHB, which is also called the Kolsky bar [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], has been used extensively to measure dynamic material properties such as the stress-strain and strain rate-strain curves of versatile materials at strain rates of approximately 10 2 -10 4 s −1 .…”

Section: Introductionmentioning

confidence: 99%

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Sound Speed and Poisson’s Ratio Calibration of (Split) Hopkinson Bar via Iterative Dispersion Correction of Elastic Wave

Shin

2022

Journal of Applied Mechanics

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A process of calibrating a one-dimensional sound speed (c_o) and Poisson's ratio (v) of a (split) Hopkinson bar is presented. This process consists of Fourier synthesis and iterative dispersion correction (time-domain phase shift) of the elastic pulse generated by the striker impact on a circular bar. At each iteration, a set of co and v is assumed, and the sound speed vs. frequency (c vs. f) relationship under the assumed set is obtained using the Pochhammer–Chree equation solver developed herein for ground state excitation. Subsequently, each constituting wave of the elastic pulse was phase-shifted (dispersion-corrected) using the c–f relationship. The co and v values of the bar were determined in the iteration process when the dispersion-corrected overall pulse profiles were reasonably consistent with the measured profiles at two travel distances in the bar. The observed consistency of the predicted (dispersion-corrected) wave profiles with the measured profiles is a mutually self-consistent verification of (i) the calibrated values of co and v, and (ii) the combined theories of Fourier and Pochhammer–Chree. The contributions of the calibrated values of co and v to contemporary bar technology are discussed, together with the physical significance of the tail part of a traveling wave according to the combined theories. A preprocessing template (in Excel®) and calibration platform (in MATLAB ®) for the presented calibration process are available online in a public repository.

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Section: Usage and Verification Of The Combined Theoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sound Speed and Poisson’s Ratio Calibration of (Split) Hopkinson Bar via Iterative Dispersion Correction of Elastic Wave

Shin

2022

Journal of Applied Mechanics

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“…The consequences of the Pochammer-Chree analysis have been studied extensively over the last 70 years, and all the important features have been verified experimentally (e.g., [5][6][7][8]). Furthermore, numerical and experimental studies have demonstrated that, if the energy of high-frequency components in a signal is not too high, a transient pulse propagating in a bar of finite length behaves essentially in accordance with the predictions of the Pochammer-Chree analysis [5,[9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Full correction of first-mode Pochammer–Chree dispersion effects in experimental pressure bar signals

Tyas

Pope

2005

Meas. Sci. Technol.

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Frequency domain analysis of dispersed strain signals in pressure bars has been an active area of study for many years. Over the last two decades, methods have been developed for the correction of dispersed signals, by adjustment of the phase angles of the Fourier components of the signal. Recent work has shown that, theoretically, dispersion correction should be significantly improved by the application of additional correction factors to the amplitude of the Fourier components. This paper describes a study using experimental and related numerical work to further test these proposals.

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“…This is known as the 'cut-off frequency'. Curtis (1954) was the first to experimentally observe secondmode dispersion in a cylindrical bar. Here, a HPB was placed at the end of a shock tube and a step-like loading function was generated through reflection of a shock generated in the tube off the end of the HPB.…”

Section: Multi-mode Propagation Theorymentioning

confidence: 99%

A review of Pochhammer–Chree dispersion in the Hopkinson bar

Rigby

Barr

Clayton

2018

Proceedings of the Institution of Civil Engineers - Engineering

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This paper presents a detailed review of the current state of the art in Hopkinson pressure bar (HPB) data analysis. In particular, the underlying theory of the HPB is discussed, and methods of correcting signals for Pochhammer-Chree dispersion and other associated effects are described. The theory of multiple mode propagation is presented, followed by a review of the current methods for correcting multiple mode dispersion, which are especially pertinent when using the HPB as a dynamic force transducer to measure rapidly changing loading events such as explosive blast loads.

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Second Mode Vibrations of the Pochhammer-Chree Frequency Equation

Cited by 16 publications

References 2 publications

Sound Speed and Poisson’s Ratio Calibration of (Split) Hopkinson Bar via Iterative Dispersion Correction of Elastic Wave

Sound Speed and Poisson’s Ratio Calibration of (Split) Hopkinson Bar via Iterative Dispersion Correction of Elastic Wave

Full correction of first-mode Pochammer–Chree dispersion effects in experimental pressure bar signals

A review of Pochhammer–Chree dispersion in the Hopkinson bar

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