Resonant ultrasound spectroscopy applications: Beyond canonical geometry

Resonant ultrasound spectroscopy (RUS) is a technique that uses a combination of experimentally measured resonant frequencies and physics-based computation of these frequencies to determine the entire set of single crystal elastic constants of a material. Computation of the resonances is most often accomplished using the Rayleigh–Ritz energy minimization method but this requires knowledge of mass density and analytical representation of the shape of the material. As a result, the sample will be manufactured into a canonical geometry such as cylinder or a rectangular parallelepiped such that its displacement field can be represented by a set of basis function. In this approach, deviation from a perfect canonical geometry can have a significant impact on the estimate elastic constants during the inversion. To overcome this limitation, this project describes a finite element method combined with x-ray computed tomography to model a sample with complex shape for computation of resonance frequencies and in the inversion of the elastic constants.