PNNL

Abstract

If a suitable number of the resonance frequencies of an elastic object are known, in principle, one can deduce a number of its physical properties like elastic constants, density, dimensions, shape , etc. The efficient calculation of the resonance frequencies is required for the effective application of resonant ultrasound spectroscopy (RUS) to determine the revelant properties of an elastic object. However, general analytic expressions are not available for the normal node free vibrations of a body with arbitrary shape and elastic properties. It was noticed by Holland and Demarest that a simple variational principle can be applied to compute the normal mode frequencies of elastic body with free boundaries. Based on this variational method, Visscher et al. developed the XYZ algorithm which can be applied to compute the resonance frequencies of a body with arbitrary shape and elastic properties. Since layered systems are finding increasing use in engineering applications, computational studies ae being carried out here to investigate the suitability of RUS as an NDE technique to determine imperfections in a layered system. Specifically, the normal mode frequencies of a four-layered sphere are computed here by the XYZ algorithm. It will be shown tht the deviations from specified layer properties cause noticeable effects on the resonant frequencies.