Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections

In order to enhance the vibration reduction capacity in a wide frequency range, a novel acoustic metamaterial beam with periodically variable cross-sections is designed by combining the mechanisms of the Bragg scattering and the locally resonant band-gaps. The spectral element method (SEM) is extended to investigate the band-gap properties of the novel acoustic metamaterial beam. Based on the exact frequency responses obtained by solving the spectral equations in the frequency domain, it is found that the interaction of the Bragg scattering and the locally resonant band-gaps can enlarge the band-gap widths. More band-gaps can be achieved if the material periodicity is harmonized with the cross-section periodicity. When these two kinds of band-gaps exist simultaneously, the locations of the locally resonant band-gaps do not strictly correspond to the resonator's natural frequencies. The width and the attenuation ability of the Bragg scattering band-gaps become wider and stronger with the increase of the ratio of the cross-sectional sizes of the two sub-cells. The experimentally measured band-gap positions and widths agree very well with the SEM results, which guarantees the correctness of the numerical results.