Acoustic Resonance Spectroscopy for Elastic Spheroids of Varying Aspect Ratios,and the Level Crossing Phenomenon

摘要

Using a T-Matrix code, the frequencies (both fundamentals and overtones) of theresonances are calculated as excited by an end-on incident plane wave. Aspect ratios of the tungsten carbide spheroids range from b/a = 1 (sphere) to 4 in steps of 0.25. The resonance frequencies are presented in the form of an acoustic spectroscopic level scheme. They are expressed in units kb (b = semimajor axis) and correspond to resonating surface waves as they form standing waves around the meridional circumference. While for the resonating Rayleigh waves the resonances frequencies only rise gradually with increasing aspect ratio, those for the Whispering Gallery waves rise much more rapidly, and hence successively cross over the various overtones of the Rayleigh resononces. This phenomenon is explained on the basis of the different character of the dispersion curves (phase velocity versus frequency) for the Rayleigh and the Whispering Gallery waves, as calculated in an exact fashion for a tungsten carbide (WC) sphere and used locally on the spheroids.