  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.
