Acoustic spectrogram and complex-frequency poles of a resonantly excited elastic tube

Abstract

We present a study of the resonance scattering undergone by an air-filled hollow elastic cylinder excited by an incident plane acoustic wave. We construct the boundary value problem, obtain its classical solution, the solution based on the Resonance Scattering Theory (RST), and generate a variety of useful computed results, some of which are later compared to experimental observations recently performed in France. We present highly accurate expressions for the phase and group velocities and for the phase and group attenuations of the first few surface waves circumnavigating (the extreme cases) of rigid and soft cylinders, and display these dispersion plots in all instances. We analyze the modal backgrounds and modal resonances of the shell, display them in a wide spectral band, determine the SEM-type pole-position diagram in the complex k1a plane, and obtain and display the background-suppressed cross section of the tube. This result serves to generate the acoustic spectrogram of the shell as well as to show the excellent agreement of this theoretical prediction with the experimental observations carried on in France. We analyze cross-sectional poles and cross-sectional dips, and reduce many of the present shell results to particular cases for impenetrable cylinders and solid elastic cylinders. For these latter ones, we obtain the dispersion plots for the phase and group velocities of the internal surface waves revolving around them. We determine expressions for the nearfield shell cross sections at different ranges, and compare them to the usual farfield results. We determine the sound pressure levels transmitted into the shell’s interior, and exhibit the controlling role the tube resonances have on the isobaric contours. We display extensive computerized calculations to illustrate all these points. Comparisons with experimental observations are shown to be quite favorable, particularly for the background-suppressed shell cross section, and for its acoustic spectrogram.