Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes

One-dimensional propagation of a longitudinal wave through an infinite piezoelectric periodically layered structure is considered. The unit cell consists, in general, of piezoelectric multilayers separated by thin electrodes which are connected through a capacitor with capacity Cj that plays the role of the external electric control providing tunability of the mechanical properties. The main focus of the present study is on the effective properties characterizing the homogenized medium. Due to the electric boundary conditions, the 4×4 transfer matrix M through the period T can be reduced to 2 × 2 dimension governing the mechanical fields only. As a result, the homogenized medium is pure elastic though its effective material parameters depend on the piezoelectric and dielectric coefficients of the actual piezoelectric medium, as well as on Cj. The effective parameters and the impedance in the low-frequency limit ω→0 and at finite frequency are obtained and analyzed.