A general approach for dispersion relations in multilayered structures with an arbitrary number of piezoelectric layers and elastic layers

A general approach, which can efficiently and automatically derive dispersion relations for infinite layered structures with any number of piezoelectric and elastic layers, is proposed in this paper. Based on the Stroh formalism and the dual variable and position method, the general relationship between top and bottom variables of a single layer is obtained first. Considering the different layups possibly appearing in multi-structures, three base cases are presented in detail. By combining these base cases repeatedly from the bottom of the plates to the top, we can easily write programming codes to derive dispersion relations for any general multilayered structure automatically. To verify this approach, dispersion curves and mode shapes for the film bulk acoustic resonator and the stacked crystal filter are presented in this paper. The results show good conformity with reported works and simultaneously prove the ability of our approach for complex and generally anisotropic multilayered structure. Above all, this general approach is efficient and superior to get the dispersion relations, which is convenient for further study of wave propagation characteristics in general multilayered structures.