Propagation and filtering of elastic and electromagnetic waves in   piezoelectric composite structures
  In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of stop bands are studied in detail. We will also analyze the reflection and transmission associated with the problem of scattering of an elastic wave by a heterogeneous piezoelectric stack. Special attention is given to the occurrence of transmission resonances in finite stacks and their dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric checkerboard structure is subsequently introduced, for which the dispersion surfaces for Bloch waves have been constructed and analysed, with the emphasis on the dynamic anisotropy and special features of standing waves within the piezoelectric structure. 
Domenico Tallarico, Natalia V. Movchan, Alexander B. Movchan, Michele   Camposaragna
cond-mat.mtrl-sci