Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with mechanically and dielectrically imperfect interfaces

• The mechanical and dielectric imperfect interfaces are both considered.
• The in-plane Bloch waves and anti-plane Bloch waves are both considered.
• The oblique propagation and normal propagation situations are both considered.
• The influences of dielectric imperfect interfaces on dispersive nature are first considered.
• The evolutionary decoupling process of QP wave with QSV wave is first reported.

The effects of mechanically and dielectrically imperfect interfaces on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied in this paper. Six kinds of imperfect interfaces between two different piezoelectric materials constituting the phononic crystal are considered. These imperfect interfaces include: the mechanically compliant dielectrically weakly conducting interface, the mechanically compliant dielectrically highly conducting interface, the grounded metallized interface, the low dielectric interface, the tangent fixed interface and the tangent slippery interface. Based on transfer matrices of piezoelectric slabs and imperfect interfaces, the total transfer matrix of a typical single cell in the periodical structure is obtained. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. In the case of normal propagation of elastic waves within piezoelectric slabs, the analytical expressions of the dispersion equations are derived and compared with other literatures. The influences of mechanically and dielectrically imperfect interfaces on the dispersive relations are discussed based on the numerical results.