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High-frequency normal mode propagation in aluminum cylinders

July 7, 2009

Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.

Publication Year 2009
Title High-frequency normal mode propagation in aluminum cylinders
DOI 10.3133/sir20095142
Authors Myung W. Lee, William F. Waite
Publication Type Report
Publication Subtype USGS Numbered Series
Series Title Scientific Investigations Report
Series Number 2009-5142
Index ID sir20095142
Record Source USGS Publications Warehouse
USGS Organization Central Energy Resources Science Center