Ultrasonic Guided Waves in Thin Orthotropic Layers: Exact and Approximate Analyses

Abstract

Exact and approximate analyses of ultrasonic guided wave propagation in thin orthotropic layers are presented in this work. Exact solutions to the equations governing the dependence of guided wave propagation speeds on the elastic constants characterizing the anisotropic properties of the layers are presented and compared with the predictions of first order approximate theories for extensional and flexural waves in thin plates. Comparison with available experimental results for dispersion of these waves in thin sheets of different types of papers leads to the confirmation or modification of the elastic constants and density reported for these papers. A particular focus of this study is the coupling of three types of guided waves (extensional (S), flexural (A), and shear-horizontal (SH)) due to anisotropy of the material. It is shown that there are significant changes in the dispersion characteristics of these modes at certain frequencies, which can be exploited to measure the in-plane elastic properties of thin layers. Another focus is to study the limitations of approximate results when compared with exact solutions for wave propagation in different directions. In general good agreements are found at low frequencies.