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

Abstract A three-dimensional cubical piezoelectric phononic crystal is theoretically studied in this paper, formed by pre-stressed piezoelectric rectangular blocks and imperfect interfaces. Firstly, transfer matrices of pre-stressed piezoelectric rectangular blocks and imperfect interfaces are obtained based on the structural characteristics. The Bloch waves consist of three groups of sub-coupled elastic waves corresponding with three orthogonal periodical directions in the three-dimensional periodical structure. Furthermore, based on the transfer matrices of typical single cell and the Bloch theorem, it is established that the theoretical model of above-mentioned three-dimensional cubical piezoelectric phononic crystal to obtain the dispersion relations of Bloch waves. Finally, the influences of non-dimensional geometrical parameters (structural and modal parameters) and physical parameters (initial stress and mechanically and dielectrically imperfect interface parameters) on the dispersion relations are discussed based on the graphically numerical results. Numerical calculation results show that the existences of initial stresses and mechanically and dielectrically imperfect interfaces equivalently lead to the alterations of structural flexibilities or rigidities. The theoretical model and numerical discussions will provide a direct guidance of multi-material additive manufacturing for pre-stressed and inhomogeneous periodic structures with partial and global dispersion properties.