Hierarchical phononic crystals with broad band gaps in low frequency by using homogenization theory

Abstract

In this study, we propose a hierarchical phononic crystal that has broad band gaps in low frequency range. In recent years, there have been a growing interest in wave filtering by using periodic composites called phononic crystal. However, conventional phononic crystals have a clear limitation that they must be thick in order to make band gaps in low frequency range. Therefore, we apply a multi-layered model with hierarchical structure to handle the problem of conventional phononic crystals. As a first step of designing, through the analytic solution of band gaps, we predict the properties of band gaps in relation to design parameters such as filling fraction, unit length and material parameters of two interlacing layers. Numerical simulations give us an optimal strategy to design a hierarchical phononic crystal from the viewpoint of broadening band gaps in low frequency regime. The underlying physics of the design can be explained by applying a mathematical theory of homogenization.