2D theory for analysis of surface acoustic waves coupled with extensional mode in finite elastic solids

To meet the increasingly critical needs in the accurate analysis of surface acoustic waves propagating in smaller resonators, a two-dimensional theory similar to popular plate theories for bulk acoustic waves in plates has been established. As part of the continuing effort in the improvement of the two-dimensional theory, we include extensional modes, which exist in finite plates and have strong effect like appearing as leaky modes with large displacements in the depth of substrates, for the better accommodation of such modes in addition to the dominant surface wave modes we are familiar with. The extra displacement components with constant amplitude in the thickness direction will account the energy leaking in a much better way with important applications in the refinement of the analysis and design of surface acoustic wave resonators. Numerical examples in a finite isotropic solid are given for the velocity and displacements to demonstrate the solution procedure and the relatively weak coupling of the extensional and surface wave modes.