The mechanism of adjusting the low-frequency ultra-wide band gap within lightweight spherical superstructue

Conventional resonant structures can be effective in obtaining broadband, but it is still a challenge to design small-sized and lightweight acoustic metamaterials with a low-frequency ultra-wideband. This paper proposes a new approach of designing a lightweight spherical localized resonance superstructure with adjustable stiffness ratio, and the mechanism of adjusting the low-frequency ultra-wide forbidden band is revealed. Then, the correlation between the zero value of its dynamic equivalent mass and the stiffness ratio of the system is studied. It is found that not only is the upper bound of the negative mass effectively broadened, but also the lower bound is successfully lowered only by adjusting the stiffness ratio of the sphere. Most importantly, based on the regulation mechanism with adjustable stiffness ratio, the lower boundary of the band gap is lowered from 171 Hz to 141 Hz, and the upper boundary is increased from 445 Hz to 710 Hz. Therefore, the low-frequency ultra-wideband of 141–710 Hz is obtained only by adjusting the stiffness ratio of the system and the Finite Element Method, which is highly consistent with theoretical analyses. Obviously, the mechanism of obtaining the low-frequency wideband through adjusting the stiffness ratio not only provides a novel idea for adjusting the low-frequency ultra-wideband, but also provides theoretical guidance for the developing the small-size and lightweight acoustic devices, so it would have potential application in the field of vibration and noise reduction.