High-frequency analysis of longitudinal wave bands in tunable rod-type piezoelectric phononic crystals

The model of tunable rod-type piezoelectric phononic crystals is established by utilizing the longitudinal effects of the piezoelectric rods for electromechanical coupling. A modified transfer matrix method (MTMM) is presented on basis of the Mindlin-Herrmann rod theory for modeling longitudinal wave motions in structural members and the method of reverberation-ray matrix (MRRM) for deriving the member transfer relations. The joint transfer relations are derived from the continuous conditions of generalized displacements and forces in adjacent members of the joints. The global transfer relation of the unit cell is then derived by considering the member and joint transfer relations in succession, from which the dispersion relation is obtained by virtue of Floquet-Bloch theorem. Numerical examples are given to validate the proposed method and to show the variation of the longitudinal-wave bands with the electrical conditions on the electrodes.