A General Method for Solving Dispersion Relations in Layered Structures with Piezoelctric and Elastic Layers

A general approach, which can derive dispersion relations efficiently and automatically for infinite layered structures with any number of piezoelectric and elastic layers, is proposed in this paper. Based on Stroh formalism and dual variable and position method, the general relationship between top and bottom variables of single layer is obtained firstly. Considering those different layups possibly appearing in multilayered structures, three base cases are presented in detail. By combing 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 structures automatically. The results show great conformity with the reported work 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.