Investigation on enhanced band-gap properties of 2D hierarchical phononic crystals

Abstract

Phononic crystals have garnered considerable attention in recent years for their unique band-gap properties, which can effectively manipulate the propagation of acoustic and elastic waves. This research focuses on exploring richer band gaps and utilizing band gap characteristics to achieve structural vibration reduction. In this study, a novel two-dimensional (2D) hierarchical phononic crystal with rich periodicities is proposed, which possesses enhanced band-gap properties. The research method used for the proposed structure is numerical simulation using the finite element method (FEM). By applying Bloch’s theorem, FEM is a more convenient tool for calculating the band gap of structures. Based on the numerical results, it can be concluded that the band gaps of the proposed 2D hierarchical phononic crystal can be classified not just into full and directional band gaps, but also into more fascinating categories based on the vibration patterns of macro and micro unit cells, which are referred to as Type I, Type II and Type III band gaps. Furthermore, the impact of structural parameter variations on the band gap is also studied, and results indicate that appropriate adjustments to the structural parameters (such as the number of unit cell n, the angle θ and the length l1) can lead to low-frequency shift and bandwidth increase in certain band gaps. A prototype of the hierarchical phononic crystal is manufactured using the 3D printing technique. Vibration tests are conducted and the simulation and experimental results are compared to verify the vibration reduction performance of the 2D hierarchical phononic crystal. The important contribution of this study is to reveal an interesting band gap generation characteristic of 2D hierarchical phononic crystals, which is beneficial for promoting understanding of the band gap mechanism in periodic structures. The enhanced band-gap properties in hierarchical periodic structures provide more potentialities and possibilities for practical vibration and noise reduction applications.