Resonant ultrasound spectroscopy in complex sample geometry
Fig, Matthew Kenneth.
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Resonant Ultrasound Spectroscopy (RUS) is the study of the mechanical resonances, or normal modes, of elastic bodies to infer material properties such as the elasticity matrix. This powerful technique is based on two physical facts, the first of which is that the resonant response of an elastic object depends on several parameters intrinsic to the object, such as the object's shape, density, elastic constants, and crystallographic orientation. The second is that using these parameters, the resonant spectrum of an object can be calculated. This method has widely been applied to rectangular parallelepipeds (RPPDs) because the use of such simple geometry frees an investigator interested only in acquiring the elastic constants of a particular material from the hindrance of dealing with the additional computational difficulty imposed by more complex sample geometry. In addition to the use of RPPDs, some work has been done with other objects of high symmetry such as cylinders and spheres. The goal of this research was to explore the extension of RUS techniques to objects exhibiting more complex shape. Toward this end, a computational method was developed for handling the addition of complex geometry. This computational scheme was then verified experimentally through the examination of several objects exhibiting complex shapes.