The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials

Abstract

In this paper, the phononic band structures of Bragg scattering and locally resonant pentamode metamaterials (PMs) with single and composite materials symmetric double-cone elements (SDCEs) are calculated by using the finite element method. The numerical results show that, for the Bragg scattering PMs with single material SDCEs, the phononic band gaps (PBGs) can be obtained while the top touch cone diameters (TTCDs) (i.e. d) are much smaller than the bottom touch cone diameters (i.e. D), and the variation range of the PBGs frequency is mainly determined by the TTCDs. This indicates that the Bragg scattering PMs with single material SDCEs can be investigated as a phonon crystal. On this basis, the locally resonant SDCE PMs can be designed by using the composite SDCEs instead of single material SDCEs, and the PBGs can be obtained under the 100 Hz. This finding provides a way to control the low-frequency acoustics waves by using small-sized SDCEs PMs. In addition, compared with the Bragg scattering PMs, the relative bandwidth of the first PBGs of the locally resonant PMs can be expanded at least 25 times. In the end, the effect of mass density and Young’s modulus E of the composition material parameters of locally resonant SDCEs PMs on the PBGs is also studied by changing the parameters individually. The results show that the lower and upper edge and relative bandwidth of the first PBGs of locally resonant PMs with composite SDCEs are mainly impacted by the difference of the mass density between the two constituent materials, and the difference of the Young’s modulus E between the two constituent materials has little effect on the PBGs.