Pentamodal property and acoustic band gaps of pentamode metamaterials with different cross-section shapes

•Pentamode metamaterials with different cross-section shapes are proposed.•Phonon band structures are calculated to analyze B/GB/G and bandgaps.•Geometrical parameters of unit can modulate pentamodal property and bandgaps.•Triangle case has excellent pentamodal property with the highest B/GB/G.•Triangle case has bandgap with lower frequency and broader bandwidth.

Pentamodal property and acoustic band gaps of pentamode metamaterials with different cross-section shapes, including regular triangle, square, pentagon, hexagon and circle, have been comparatively studied by finite-element method. Results show that for the varying diameters of circumcircles in thick and thin ends of unit (D and d  ), the ratio of bulk modulus to shear modulus (B/GB/G) and bandgaps of these five structures perform similar changing tendency. With the increasing d  , B/GB/G decreases and the single-mode bandgap moves toward high-frequency direction with the decreasing normalized bandwidth (Δω/ωgΔω/ωg). With the increasing D  , B/GB/G keeps around the respective average value, and the single-mode bandgap firstly moves to high-frequency then to low-frequency direction with the firstly increasing and then decreasing Δω/ωgΔω/ωg. Complete bandgap appears as D reaching to critical value for each given d  , then moves to high-frequency direction. For same parameters the triangle case has highest B/GB/G and acoustic band gaps with lower frequency and broader bandwidth.