Propagation of elastic longitudinal waves in a periodic piezoelectric-piezosemiconductor rod

Abstract

To investigate the elastic wave propagation properties in the periodic piezoelectric semiconductor(PS) rods, based on Hamilton's variational principle, the Love-type rod equations for PS rods are derived, and the state equations for piezoelectric and PS rods are obtained, respectively. For a unit cell made of a piezoelectric rod and a PS rod, using the continuity condition of the unit cell's interface, the transfer matrix for the state vectors, including the axial displacement, electric potential, axial stress, and axial electric displacement at the two surfaces of the unit cell, are established. The dispersion equation is derived using the Bloch theorem. Numerical results show that the band structure modulation can be achieved by changing the initial electron concentration, the length ratio, and the rod radius of the PS phase in a cell. For instance, the first band gap moves down with the increasing initial electron concentration, the length ratio, and the radius of the PS rod. It provides theoretical guidance for designing novel periodic PS structure-based devices.