Vibration Transmission Characteristics of Bistable Nonlinear Acoustic Metamaterials Based on Effective Negative Mass.

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of 2. The external excitation amplitude