含共振单元的单相3维声子晶体设计及其带隙特性研究

局域共振型声子晶体具有低频段的弹性波带隙特性，在振动与噪声控制工程领域有着重要的应用前景。三维局域共振型声子晶体的结构形式目前主要是基于多组元材料体系，在面向工程实际的制造和应用方面存在局限。对此，本文提出一种可实现低频局域共振带隙的单相三维声子晶体结构，利用有限元方法计算了声子晶体的能带结构、振动模态和传输特性。结果表明：该结构在具有高频带隙的同时，可在归一化频率低于0.1的范围内打开相对带隙宽度超过20%的低频弹性波带隙。结构中球形质量单元和连接体的局域共振是该低频带隙产生的主要原因。结构材料属性的变化影响带隙频率值的实际大小，而结构几何参数决定带隙在整个能带结构中出现的相对位置。通过改变结构材料参数和几何参数，可以实现对低频带隙边界和带隙宽度的调控。带隙的进一步拓宽可以通过构造几何参数渐变的组合结构来实现。本文所提出的单相三维声子晶体结构可用于低频减振降噪材料和器件的设计开发。

Design of Single Phase 3D Phononic Crystal with Resonantor and Research of Band Gap Property

The locally resonant phononic crystals have low frequency elastic bandgap characteristics and have important application prospects in the field of vibration and noise control. The structure of three-dimensional locally resonant phononic crystals is mainly based on a multi-component material system, which limits its manufacturing and application for practical engineering. Therefore, a three-dimensional phononic crystal structure composed of single-phase material is proposed. The band structure, vibration mode and transmission spectrum of the phononic crystals are calculated by finite element method. The numerical results show that the structure can open a 20% complete bandgap within the range of normalized frequency below 0.1. The local resonance of the spherical mass element and the connectors is the main cause of the bandgap. The change of structural material properties affects the frequency of the bandgap, and the structural geometric parameters determine the relative position of the band gap in the whole band structure. The width and position of phononic band gaps can be manipulated via the materials and geometric parameters of the structure. In addition, the further widening of the band gap can be realized by constructing gradient structures with gradually changing geometric parameters. The three-dimensional structure composed of single-phase material can be used for the design and development of low-frequency vibration and noise reduction materials and devices.