Complete low-frequency bandgap in a two-dimensional phononic crystal with spindle-shaped inclusions

• Published in: Chinese physics B 2016-04, Vol.25 (4), p.284-291
• Main Author: 王婷 王辉 盛美萍 秦庆华
• Format: Article
• Language: English
• Subjects: Energy gaps (solid state); Inclusions; Low frequencies; Mathematical models; Sensitivity analysis; Theorems; Two dimensional; Wave attenuation; 二维; 低频噪声; 包裹体; 声子晶体; 完全带隙; 布洛赫定理; 纺锤状; 频率范围
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/25/4/046301

A two-dimensional phononic crystal （PC） structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover, the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.