Dispersion relations of elastic waves in three-dimensional cubical piezoelectric phononic crystal with initial stresses and mechanically and dielectrically imperfect interfaces

•The theoretical model of a 3D cubical piezoelectric phononic crystal has been established.•Contrastive influences of non-dimensional structural and modal parameters have been considered.•Contrastive influences of initial stresses and imperfect interfaces have been considered.•Properties of partial and global dispersion relations have been discussed.