Guided Wave Propagation in a Layered Half-Space Structure of Anisotropic Materials

Layered half-spaces are widely used in engineering particularly for structures working under extreme conditions or having specific surface requirements. The thin layer helps improve engineering properties for the substrate material and prevent external damages caused by weather condition, friction, or chemical corrosion. Ultrasonic guided waves have been shown the advantages in material characterization and nondestructive evaluation of layered media that have a large dimension, include hard-to-reach areas, or are buried. In this paper, the motion of Rayleigh surface waves in layered half-spaces modeled as an orthotropic layer overlying an orthotropic half-space is investigated. The explicit expressions of free Rayleigh waves in both the layer and the half-space are first presented. Using the boundary conditions on the free surface and at the interface, the dispersive relations of Rayleigh waves are derived resulting in the dispersion curves. Reciprocity theorems are then applied to acquire the exact solutions of Rayleigh waves in coated structures of anisotropic materials under time-harmonic loads. The closed-form amplitudes of surface waves are found by using reciprocity theorems between two states, the Rayleigh wave that is generated by the time-harmonic forces and a free Rayleigh wave traveling in the layered structures.