Resonant ultrasound spectroscopy applications: Elastic moduli computation with x-ray computed tomography input for irregularly shaped objects.

Resonant ultrasound spectroscopy 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 moduli of the material. Computation of the resonances is most often accomplished using the Rayleigh-Ritz energy minimization technique, and a basis function that requires sample with canonical geometry, such as a cylinder or a rectangular parallelepiped. Any deviation from canonical geometry can have a significant impact on the calculated resonance frequencies and the inverted elastic moduli. To overcome this limitation, this paper describes an approach that uses x-ray computed tomography data to generate accurate solid part model of components with complex geometry. The part model is then imported into an off-the-shelf finite element method (FEM) software to perform the forward problem. The FEM was combined with surrogate modeling for computation of resonance frequencies of both canonical and non-canonical samples, and ultimately, the inversion of elastic moduli.