The experimental realization and theoretical understanding of a two-dimensional multiple cells lumped ultrathin lightweight plate-type acoustic metamaterials structures have been presented, wherein broadband excellent sound attenuation ability at low frequencies is realized by employing a lumped element coupling resonant effect. The basic unit cell of the metamaterials consists of an ultrathin stiff nylon plate clamped by two elastic ethylene-vinyl acetate copolymer or acrylonitrile butadiene styrene frames. The strong sound attenuation (up to nearly 99%) at low frequencies is experimentally revealed by the precisely designed metamaterials, for which the physical mechanism of the sound attenuation could be explicitly understood using the finite element simulations. As to the designed samples, the lumped effect from the frame compliance leads to a coupling flexural resonance at designable low frequencies. As a result, the whole composite structure become strongly anti-resonant with the incident sound waves, followed by a higher sound attenuation, i.e., the lumped resonant effect has been effectively reversed to be positive from negative for sound attenuation, and the acoustic metamaterial design could be extended to the lumped element containing multiple cells, rather than confined to a single cell.

We present an ultra-broadband acoustic metamaterial with inhomogeneous high-order Fabry–Pérot (FP) resonances that achieves near-perfect continuous absorption in the range of 400–10000 Hz. The unit is composed of multiple FP channels with inhomogeneous cross-sectional areas, allowing for flexible adjustment of the impedance characteristics of each channel. This approach prevents the high-order peaks’ resistances from increasing rapidly and ensures a smooth resistance characteristic across a broad frequency range. As a result, the absorption performance in the high-frequency range above 3000 Hz can be significantly enhanced, eliminating the need for conventional porous materials. The inhomogeneous high-order absorption mechanism is investigated thoroughly by theoretical calculations and finite element simulations. By critically coupling the FP channels, a 27-cell broadband metamaterial is obtained with an average absorption coefficient above 90% over 400–10000 Hz, which is verified by experiments in a square impedance tube and an alpha-cabin reverberation room, respectively. Characterized by its extraordinary performance and easy-fabricated structure, this metamaterial has great potential in noise control engineering applications, especially in environments with low temperature, high humidity, or significant dustiness.

A theoretical model of a new type of two-degree-of-freedom local resonance mass-spring system with the resonator considering vertical and rotational vibration (the moment of inertia) is proposed to generate a negative effective mass over specific frequency ranges. Based on the theoretical analysis, a novel elastic metamaterial plate is designed. The flexural vibration band structures as well as the transmission spectrum of the metamaterial plate are investigated by using the finite element method. Subsequently, the formation mechanism of the band gaps is analyzed by studying the displacement field of the eigenmodes at the band gap edges. At last, the effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied and discussed in detail. The related results well confirm that the two-degree-of-freedom metamaterial shows negative mass density in two distinctive asymptotic regions, and the proposed elastic metamaterial plate has two FVBGs with the total width of 94.45 Hz below 200 Hz. The magnitude of torques introduced into the local resonance system can obviously affect the locations of the FVBGs. For the elastic metamaterial plate with thick local resonance lead plate and weak rubber is appropriate to obtain a lower gap, but the total width of the FVBGs becomes narrow. However, it does just the opposite for the condition with thin local resonance lead plate and strong rubber. For the double-side stubbed plate, it can enhance the coupling of the flexural traveling wave and the local resonance modes, which can greatly enlarge the bandwidths. The new working mechanism and the related calculation results of the designed structures would provide an effective way for elastic metamaterial plate to broaden the FVBGs at low frequencies, which has potential applications in low-frequency vibration and noise attenuation.