Comparison of the modal properties of a stiff layer embedded in a solid medium with the minima of the plane-wave reflection coefficient

Abstract

Waves which propagate along embedded layers offer potential for the nondestructive characterization of the layers and of the boundary conditions between the layers and the embedding medium. However, it is known that the minima of the reflection coefficient, popularly used to measure the modal properties of leaky waves in plates immersed in fluids, do not correlate precisely with the dispersion curves and may be particularly misleading when the embedding medium is solid and of the same order of impedance as the layer. This paper is the first of a pair which study the practical case of a thin solid layer which is embedded at the bondline of a diffusion bonded titanium joint and is slightly stiffer than the titanium. In this paper the modal properties of the layer are compared with the plane-wave reflectivity; the second paper [J. Acoust. Soc. Am. 97, 1638–1649 (1995)] addresses the near-field response of the system to a finite acoustic beam. It is demonstrated in this paper that the loci of the reflection coefficient minima are related to the dispersion curves in wave-type groupings, but that they do not match in a direct manner. The divergence of the loci from the dispersion curves appears to increase with the rate of leakage of the modes which in turn is related inversely to the acoustic impedance contrast between the layer and the embedding medium. Therefore the loci of the plane-wave reflection coefficient minima should not be used to plot the modal properties of the system. Nevertheless, it is recognized that the loci are potentially useful for the characterization of the embedded layer since they are sensitive to changes in the properties of the layer.