Phononic band structure and figure of merit of three-dimensional anisotropic asymmetric double-cone pentamode metamaterials
Authors: Cai Cheng-Xin , Chen Shao-Geng , Wang Xue-Mei , Liang Jun-Yan , Wang Zhao-Hong ,   Key Laboratory of Grain Information Processing and Control (Henan University of Technology), Ministry of Education,  Zhengzhou 450001, China,   Henan Provincial Key Laboratory of Grain Photoelectric Detection and Control, Henan University of Technology, Zhengzhou 450001, China,   College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China,   School of Electronic and Information Engineering, Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China
Published: December 2020

<sec> Pentamode metamaterial (PM) is a kind of artificial microstructure extremum material with solid morphology and fluid properties proposed by Milton and Cherkaey. By decoupling the compression and the shear waves, the periodic structure is difficult to be compressed, but the shear deformation occurs easily. Theoretically, acoustic metamaterials consisting of such periodic arrangement of structural units can achieve complete matching with water. Therefore, the characteristics of adjustable modulus anisotropy, small stuffing rate and broadband endow the PMs with excellent acoustic control ability, which has attracted more attention of researchers.</sec><sec> In this paper, the narrow-diameter intersection point <i>P</i> (0.25<i>a</i>, 0.25<i>a</i>, 0.25<i>a</i>) of an isotropic three-dimensional PM selected as the reference point in four different directions (X-axis, Y-axis, Z-axis and body diagonal). When the <i>P</i>-point moves, the farther the <i>P</i>-point is, the greater the degree of anisotropy is. The introduction of anisotropy will cause the structural bifurcation of the three-dimensional PM to change structural parameters, and the structural parameters are important factors affecting the band characteristics of the three-dimensional PM of Bragg scattering. In order to study the influence of anisotropy on the band structure and pentamode properties of three-dimensional asymmetric double-cone PMs, we use the finite element simulation software COMSOL to calculate the primitive-cell of three-dimensional anisotropic PMs under Bloch boundary conditions. </sec><sec> By adjusting the position of <i>P</i> point, four different types of three-dimensional anisotropic asymmetric double-cone PMs are constructed. Since the anisotropy changes in different directions have different effects on the parameters of the asymmetric double-cone structure, the band characteristics and the pentamode characteristics will also receive different degrees of influence. In this paper, the relationship between the degree of anisotropy and the band gap characteristics, single-mode region and figure of merit (FOM) are given, and the result can provide guidance for the design of asymmetric double-cone PM acoustic device. Compared with the isotropic double-cone PMs, the relative bandwidth of the first band gap of the anisotropic double-cone PMs can be broadened to 123%, and the FOM can be increased to 6.9 times. Due to the introduction of anisotropy, Due to the introduction of anisotropy, the structure of three-dimensional asymmetric double-cone PMs are more complex, the demand for sample fabrication is further improved, and the stability of PMs also reduced. Therefore, PMs with high stability and easy to be fabricated still needs further research and exploration.</sec>