A two-dimensional theory for the analysis of surface acoustic waves in finite anisotropic solids

A two-dimensional theory for surface acoustic waves (SAW) analysis in finite solids is developed for anisotropic materials through the introduction of complex exponentially decaying parameters and expansion functions with the combination of trigonometric and exponential functions. Following the usual procedure for dimension reduction with three components in the basis function and complete coupling of three mechanical displacements due to anisotropy, we now have nine two-dimensional equations for the surface acoustic wave propagation in a finite anisotropic solid, resembling the higher-order Mindlin plate equations for bulk acoustic waves. We also found that these equations give the identical velocity in limiting case where the depth of the solid is infinite. With these equations and corresponding decaying parameters that are material specific and can be extracted through the half-space solutions, we calculated the phase velocity of straight-crested surface acoustic waves in a finite anisotropic strip to demonstrate the applications of these two-dimensional equations and the solution technique. Similar to plate theories, this two-dimensional theory can be used in the surface acoustic wave device modeling for both analytical and numerical solutions with the advantage of simplifying the physical model and reducing the computational difficulty, thus posing great potential in aiding the increasingly complicated but important modeling and analytical efforts.