Complex Band Structure and Dispersion Relation of Acoustic Waves in Piezoelectric Based Topological Phononic Crystals

Abstract

In present work, the acoustic band structure of a 2D phononic crystal (PC) containing piezoelectric materials (Bi12XO20, X=Si, Ge, Ti; LiTaO3) were investigated by the finite element method. 2D PC with triangular and honeycomb lattices composed of piezoelectric cylindrical rods are in the air and liquid matrix. The existence of stop bands are investigated for the waves of certain frequency ranges. This phononic band - forbidden frequency range - allows sound to be controlled in many useful ways in structures. These structure can be used as sonic filters, waveguides or resonant cavities. The calculated phonon dispersion results indicate the existence of full acoustic modes in the proposed structure along the high symmetry points. We have also calculated the band structures of the different types of unit cells that are yielded by space group symmetry operations of the triangular resonators. The results show that these acoustic metamaterials with Helmholtz resonators can be used successfully to reduce the Dirac cone frequencies. Dirac cone frequency decreases gradually with increasing filling ratio, which indicates a possible way to control wave propagation on the subwavelength scale. Numerical simulation results show that acoustic metamaterials can behave like zero-refractive-index media and can be applied to acoustic tunneling. © 2019, META Conference. All rights reserved.