Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Phononic crystals can be used to control elastic waves due to their frequency bands. This paper analyzes the passive and active control as well as the dispersion properties of longitudinal waves in rod-type piezoelectric phononic crystals over large frequency ranges. Based on the Love rod theory for modeling the longitudinal wave motions in the constituent rods and the method of reverberation-ray matrix (MRRM) for deriving the member transfer matrices of the constituent rods, a modified transfer matrix method (MTMM) is proposed for the analysis of dispersion curves by combining with the Floquet–Bloch principle and for the calculation of transmission spectra. Numerical examples are provided to validate the proposed MTMM for analyzing the band structures in both low and high frequency ranges. The passive control of longitudinal-wave band structures is studied by discussing the influences of the electrode’s thickness, the Poisson’s effect and the elastic rod inserts in the unit cell. The influences of electrical boundaries (including electric-open, applied electric capacity, electric-short and applied feedback control conditions) on the band structures are investigated to illustrate the active control scheme. From the calculated comprehensive frequency spectra over a large frequency range, the dispersion properties of the characteristic longitudinal waves in rod-type piezoelectric phononic crystals are summarized.