Pentamodal behaviors and acoustic bandgaps of asymmetric pentamode elastic metamaterials

The asymmetric pentamode metamaterial structure which is built by connecting double-cones with different cross-section shapes (regular triangle, square, pentagon and hexagon) to form diamond lattice is proposed in this paper. Then its phonon band structure is calculated by finite-element method (FEM), and its pentamodal behaviors and acoustic bandgaps are studied in detail. Results show that in the process of adjusting geometrical parameters, the asymmetric case performs similar pentamodal behaviors [ratio of bulk modulus to shear modulus B/G and single-mode bandgap (SBG)] with the symmetric cases. And the asymmetric case not only remains the intrinsic complete bandgap (CBG) of mode 12-13 like symmetric cases, but also opens new and wide CBG of mode 10-11 and mode 14-15 for appropriate parameters. Therefore, introducing structural asymmetry should be an effective way to open CBG in pentamode elastic metamaterials.