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

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.

A brief review of metamaterials for opening low-frequency band gaps

“…In general, the traditional pentamode metamaterial is able to open an elastic wave band gap whose location is dependent on its material parameters. The relationship between the center frequency of the band gap and the system parameters is given by [44]…”

“…Obviously, there are two possible ways to lower the center frequency of the band structure attained by the pentamode metamaterial, namely, decreasing Young's modulus and increasing the mass density of the material. For instance, the center frequency of the band gap shifts from 3 621 Hz to 6.5 Hz by replacing the constituent material from aluminum to rubber only [44] . Additionally, through imbedding the material element with a large density into the constituent material, for instance, incorporating the lead block into the rubber constituent material, the center frequency of the band gap can be decreased further with the increase in the effective mass density [44] .…”

“…For instance, the center frequency of the band gap shifts from 3 621 Hz to 6.5 Hz by replacing the constituent material from aluminum to rubber only [44] . Additionally, through imbedding the material element with a large density into the constituent material, for instance, incorporating the lead block into the rubber constituent material, the center frequency of the band gap can be decreased further with the increase in the effective mass density [44] . The second approach for realizing low-frequency band gaps based on the pentamode metamaterial is replacing the traditional pentamode element as an LR one.…”

Theoretical verification of three-dimensional manufacturable pentamode metamaterial microstructure

“…Inspired by the above pioneering works, other scientists also tried to further improve the mechanical property of 3D pentamode microstructure and realize the effective modulation of band gaps by changing the constituent material [16] or lattice types [17], introducing asymmetric factors [18,19], exploring other potential pentamode microstructures [20][21][22][23][24] and so on. It is noteworthy that most of the reports about pentamode are related to the classic pentamode microstructure proposed by Milton [2], and it is a diamond lattice structure formed by double-cone elements.…”

Core-shell pentamode metamaterials with broader mechanical response and higher sensitivity

“…After these pioneering works, researchers further studied the mechanical/acoustic properties of pentamode metamaterials from two aspects. One aspect is to study the influences of double-cone's geometric features, including the asymmetry factor [17,18], cross-section shape [19], constituent material [20] and so on, on the properties of diamond-like pentamode metamaterial [21]. The other aspect is to investigate the pentamodal performance for different lattice types [22][23][24], and try to find more potential pentamode microstructures with higher B/G ratio, lower frequency and broader band gap.…”