Theoretical study on phononic crystals and acoustic metamaterials with structural hierarchy

Abstract

The purpose of this study is to establish a theoretical framework on the bandgap performance and double negative effective material properties of phononic crystals with a hierarchical structure and to design the hierarchical phononic crystals for practical engineering problems. The reflection coefficients of the hierarchical phononic crystals are formulated as an exact and concise form expressed by material properties and geometrical parameters. The hierarchical phononic crystals have stopbands in wide frequency ranges compared to the conventional phononic crystals. The frequency-dependent effective material properties of the hierarchical phononic crystals are derived through a dynamic homogenization theory and double negative effective properties are obtained in a certain passband. In addition, by using the geometrical advantages of the structural hierarchy, the hierarchical phononic crystals are designed for filtering the multiple target frequencies and obtaining the target material properties with double negativity.