This paper demonstrates low-frequency vibration suppression and sound radiation of an acoustic metamaterial plate which is composed of periodical single-stage multi-degree-of-freedom (MDOF) resonators and a homogeneous plate. Dispersion relation for a unit cell and vibroacoustic performance for a simply supported metamaterial plate has been derived. Multiple band gaps can be obtained for the metamaterial plate, within which large vibration suppression and sound reduction can be achieved for the finite simply supported metamaterial plate. Analysis of the infinite and finite meta-plate implies a validation between these two theoretical methods. Low-frequency vibration suppression and sound reduction within band gaps can be attributed to the translational and rotational resonance from the attached resonators which generate inertia to counterbalance the shear force in the plate induced by the flexural wave. Study in this work shows potential in the practical application for requirements of small room installation and multiple band gaps.

本文展示了由周期性单级多自由度 (MDOF) 谐振器和均质板组成的声学超材料板的低频振动抑制和声辐射。推导出单胞的色散关系和简支超材料板的振动声学性能。超材料板可以获得多个带隙，在带隙范围内，有限简支超材料板可以实现大的振动抑制和降噪。无限和有限元板的分析意味着这两种理论方法之间的验证。带隙内的低频振动抑制和声音降低可归因于来自连接的谐振器的平移和旋转谐振，这些谐振器产生惯性以抵消由弯曲波引起的板中的剪切力。这项工作的研究显示了在小房间安装和多带隙要求的实际应用中的潜力。