Rayleigh–Ritz calculation of the resonant modes of a solid parallelepiped in a pressurizing fluid

Abstract

Resonant ultrasound spectroscopy relies on comparisons of experimentally determined vibrational spectra to theoretically computed spectra for the extraction of the elastic moduli of the solid samples. To determine the pressure dependence of these moduli, resonant spectra are taken for samples pressurized by a surrounding gas and knowledge of the contribution of the surface loading of the sample by the gas is needed in order to extract the intrinsic pressure dependence of the moduli. To facilitate the required comparisons, a Rayleigh-Ritz variational calculation of the vibrational spectrum is formulated which includes the loading of the solid by the pressurizing fluid. This formalism is used to compute the effect of gas loading on the vibrational spectrum of an isotropic, solid parallelepiped.

Gas hydrate property measurements in porous sediments with resonant ultrasound spectroscopy

“…Interpretation of RUS spectra on polycrystalline, heterogeneous geological specimens is considerably more complex [ Ulrich et al , 2002; Zadler et al , 2004]. Gas‐phase viscous coupling with the sample surface may also impact the resonance spectra when conducting measurements at high pressure [ Beck , 2004; Isaak et al , 1998]. In the present work, our interest is in monitoring relative changes in resonance response; predicting resonance peaks and extracting quantitative mechanical property information from the spectra presented in this paper is an ongoing area of research that will be the subject of a future publication.…”