To address the problem of low-frequency broadband vibration and noise encountered in engineering, a method for expanding the low-frequency band gap of locally resonant acoustic metamaterials is proposed based on the multi-mode coupling effect. A computational method for the band gap characteristics of second-order multi-mode acoustic metamaterials has been derived. By incorporating the vibrational modes obtained from band structure calculations, a systematic investigation of the formation mechanisms of multiple band gaps was conducted, revealing that the emergence of these multiple band gaps stems from the coupled resonance between elastic waves and distinct vibrational modes of the local resonator units. Furthermore, the influence of design parameter variations on the bandgap was investigated, and the strategy of realizing low-frequency multi-order bandgaps by increasing the order of local resonance units was examined. Finally, vibration tests were conducted on the second-, third-, and fourth-order multi-mode coupled acoustic metamaterials. The results demonstrated that these materials exhibit an expanded vibration band gap within the low-frequency range, and the measured frequency response aligns closely with the theoretical calculations. This type of acoustic metamaterial offers viable applicability for controlling low-frequency broadband vibrations.
Wu et al. (2025) studied this question.