Pentamode metamaterials with ultra-low-frequency single-mode band gap based on constituent materials

Abstract

Abstract An effective method for realizing ultra-low-frequency single-mode band gap in pentamode metamaterials is proposed based on constituent materials. Results show that the decreasing ratio E/ρ (stiffness/mass density) of constituent material can significantly lower the frequency range of single-mode band gap. By merely replacing the constituent material from Al to rubber, the center frequency f c of single-mode band gap can be reduced nearly 600 times (from 3621 Hz to 6.5 Hz), while the normalized bandwidth Δf/f c and the ratio of bulk modulus B to shear modulus G of pentamode structure keep substantially stable. The nonlinear fitting demonstrates that the relation between f c and E/ρ satisfies the logarithmic function. The two-component pentamode structure is designed to further explore the ultra-low-frequency single-mode band gap. The effects of thick-end diameter D of double-cone, diameter D 0 and material type of additional sphere, on single-mode band gap of two-component system are analyzed. This work is attractive for several ∼Hz acoustic/elastic wave regulations using pentamode metamaterials.