Effects of Layer Properties on the Ultrasonic Resonance of Composite Spheres

Abstract

The efficient calculation of the resonance frequencies is required for the effective application of resonant ultrasound spectroscopy (RUS) to determine the relevant properties of an elastic object. 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. However, general analytic expressions are not available for the normal mode free vibrations of a body with arbitrary shape and elastic properties. It was noticed by Holland and Demarest (1971) that a simple variational principle can be applied to compute the normal mode frequencies of an elastic body with free boundaries. Based on this variational method, Visscher et al. (1991) 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 are being carried out 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 by the XYZ algorithm. It will be shown that the deviations from specified layer properties cause noticeable shifts on the resonant frequencies.