On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers

Abstract

In this paper, dispersion of guided waves in a three-layered sandwich plate is considered. The focus here is on a configuration consisting of a thin anisotropic layer sandwiched between two identical isotropic layers. This configuration could model, for example, a superconducting tape where the middle layer is a brittle superconductor and the surrounding layers are isotropic and ductile. An approximate dispersion relation correct to O(h) governing the guided waves is obtained by expanding the field inside the thin middle layer in powers of the small thickness h of the layer. Numerical examples are given for two specific systems with superconducting middle layers. Some characteristic features, particularly at low frequencies, are investigated. Comparison between the exact and approximate dispersion relations are made to show that the approximation works well in the frequency interval of interest. The characteristic features may be useful for ultrasonic measurements of the anisotropic elastic constants of the thin layer.