The Analysis of Surface Acoustic Wave Resonators with Periodic Electrodes by Rayleigh-Ritz Method

The analysis of surface acoustic waves (SAW) in finite elastic solids with complications such as discrete electrodes and anisotropic materials is of great importance in resonator design. Due to the lack of analytical solutions from a simple and systematic procedure, various approximate methods have been employed in addition to some aggressive simplifications. In this study, with the consideration of actual resonators, the Rayleigh-Ritz method is proposed to include a large number of periodic electrodes and structural boundary conditions. The consideration of material anisotropy can be easily included in the formulation without significantly increasing difficulties in the matrices and eigenvalue computation. In addition, the displacements have been obtained with specially chosen orthogonal functions of decaying nature. The periodicity of the structure and precise geometry of electrodes and substrate can be fully considered, making the analysis superior to approximate techniques based on simplifications.