The effect of material parameter values on the relation between the energy gap width and the scatterer symmetry in two-dimensional phononic crystals

TL;DR

This study numerically investigates how lattice and scatterer symmetry, along with material parameters, influence phononic band gaps in two-dimensional solid phononic crystals with various configurations.

Contribution

It provides new insights into the relationship between material parameters, symmetry, and phononic band gap widths in different lattice and scatterer configurations.

Findings

Triangular lattices produce the broadest phononic gaps.

Symmetry matching between rods and lattice maximizes gap width in high-density rod structures.

Material parameters like velocity values have a lesser effect on gap width.

Abstract

The phononic band structures of two-dimensional solid phononic crystals with different lattice and scatterer symmetry are studied numerically, with three types of lattice (square, triangular and rectangular) and four different scatterer shapes (circle, hexagon, square and rectangle) considered. XY and $Z$ vibration modes are investigated separately. Two types of phononic crystal are considered: one composed of high-density rods embedded in a low-density matrix, the other of low-density rods in a high-density matrix. In the former case, lattice type and polarization being fixed, the broadest gaps are obtained when the symmetry of the rods corresponds to that of the lattice (the shape of a rod is identical with that of the first Brillouin zone); the largest gap width values are observed in triangular lattice-based crystals (compared to those based on square and rectangular lattices), the shape of the corresponding first Brillouin zone being closest to a circle. These rules do not apply to structures in which the density of the rod material is lower than that of the matrix. In this case, when the symmetry of the rods corresponds to that of the lattice, gaps either fail to appear at all, or are much narrower than in other configurations. The effect of other material parameter values (such as the longitudinal and transversal velocity values) on the considered relation proves much lesser.