Wave band gaps in three-dimensional periodic piezoelectric structures

The three-dimensional periodic piezoelectric composites are composed of the spheres embedded in matrix materials with the face center cubic arrangement. The electric fields are approximated as quasi-static. By the plane-wave expansion method, the band structures of BaTiO3/polymer and polymer/BaTiO3 composites are calculated. The expression of generalized eigenvalue equation is derived. The results show that it is more easily to generate the wave band gaps for piezoelectric spheres in polymer matrix than the reverse structures. The location and width of band gaps can be changed by piezoelectricity. The piezoelectric constants can influence the degenerate relation for the two lowest acoustic branches.