Research on the structural design and pentamodal property of three-dimensional multilayer cylindrical pentamode metamaterials for tuning acoustic waves

Pentamode metamaterial (PM) is an artificial solid form metamaterial with fluid characteristics. In this paper, a three-dimensional (3D) PMs based on multilayer cylindrical elements are proposed for increasing tunable structure parameters, obtaining great pentamodal property, reducing band gap frequency and decreasing connection overlap areas of elements. Compared with the PMs with double-cone elements, under the same parameters, the lower edge frequency of the single-mode band gaps can be reduced by 33.2%, the maximum value of figure of merit can be increased by 84.8% and the phononic band gaps can be reduced by 73.9%.