Study on the Existence of Band Gaps for the Transverse Mode in 2D Piezoelectric Phononic Crystals from a Point View of Connectivity

From a practical point of view, a complete band gap can be engineered to provide a vibration insulation environment for high-precision mechanical systems in a given frequency range. Understanding the band structure of piezoelectric phononic crystals can lead to improvements in the design of high performance transducers. The band structures for the transverse mode of 2D phononic crystals consisting of piezoelectric cylinders distributed periodically in a polymer matrix (1-3 connectivity), and vice versa (3-1 connectivity) are investigated in this paper, respectively. We give a brief derivation of the secular equation for the transverse vibration mode (Z mode) in which the mechanical displacements and the cylinders are parallel and perpendicular to Bloch wave vectors. Band structures are calculated to find the band gaps for both types of piezoelectric phononic crystals, which will be used to analyze the effect of connectivity of piezoelectric phonic crystals on the existence of band gaps. Numerical results reveal that the strong difference of physical properties between the constituents in piezoelectric phononic crystals can´t dominate the existence of band gaps and the connectivity of the constituents plays an important role in the mechanism. Finally the influences of cross-sectional shape and filling fraction of filling cylinders upon the existence of band gaps are studied as well.