This thesis demonstrates the practicability of using Resonant Ultrasound Spectroscopy (RUS) in combination with Finite Element Analysis (FEA) to determine the size and location of a defect in a material of known geometry and physical constants. Defects were analyzed by comparing the actual change in frequency spectrum measured by RUS to the change in frequency spectrum calculated using FEA. FEA provides a means of determining acceptance/rejection criteria for Non-Destructive Testing (NDT). If FEA models of the object are analyzed with defects in probable locations; the resulting resonant frequency spectra will match the frequency spectra of actual objects with similar defects. By analyzing many FEA-generated frequency spectra, it is possible to identify patterns in behavior of the resonant frequencies of particular modes based on the nature of the defect (location, size, depth, etc.). Therefore, based on the analysis of sufficient FEA models, it should be possible to determine nature of defects in a particular object from the measured resonant frequency. Experiments were conducted on various materials and geometries comparing resonant frequency spectra measured using RUS to frequency spectra calculated using FEA. Measured frequency spectra matched calculated frequency spectra for steel specimens both before and after introduction of a thin cut. Location and depth of the cut were successfully identified based on comparison of measured to calculated resonant frequencies. However, analysis of steel specimens with thin cracks, and of ceramic specimens with thin cracks, showed significant divergence between measured and calculated frequency spectra. Therefore, it was not possible to predict crack depth or location for these specimens. This thesis demonstrates that RUS in combination with FEA can be used as an NDT method for detection and analysis of cracks in various materials, and for various geometries, but with some limitations. Experimental results verify that cracks can be detected, and their depth and location determined with reasonable accuracy. However, experimental results also indicate that there are limits to the applicability of such a method, the primary one being a lower limit to the size of crack - especially thickness of the crack - for which this method can be applied.
