Wave Dispersion in Cylindrical Tubes: Applications to Hopkinson Pressure Bar Experimental Techniques

Abstract : It is well known that harmonic waves with higher frequencies travel slower than those with lower frequencies and that they are known as wave dispersion in finite diameter rods. From the frequency equation, the phase speed can be determined if the wavelength is known. A dispersion correction methodology uses the frequency equation to disperse a waveform to a specific location of interest. Dispersion correction methodologies are generally used in split-Hopkinson pressure bar (SHPB) techniques to reduce experimental data accurately. This report investigates wave propagation and wave dispersion in cylindrical tubes. Based on the work of Mirsky and Herrmann (M-H), the phase speed can be solved for wave motion along a cylindrical tube with a specific thickness-to-radius ratio. A numerical algorithm is developed to solve the M-H model and is compared with the solutions obtained from a three-dimensional finite element model. It is found that the first mode of the M-H solution gives the correct phase speed for wave motion in a tube. A modification to the traditional inverse fast Fourier transform algorithm is proposed for better prediction of the dispersed signal. The effects of the tube dimensions and the accuracy of dispersion correction in SHPB experiments are also discussed.

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