This paper delves into the vibration and acoustic radiation properties of a metamaterial plate integrated with grouped local resonators (GLRs). The GLRs, consisting of multiple spring-mass resonators arranged in various configurations such as series, parallel, and periodic arrangements, are shown to significantly influence the structural performance of the plate. An advanced Fourier series is implemented to articulate the displacement functions and surface acoustic pressure of the plate. By utilizing the energy principle, a vibro-acoustic coupling model is developed to describe the interaction between the metamaterial plate and the external acoustic field. The theoretical framework is rigorously validated against finite element method simulations, yielding highly congruent results. The local resonance bandgap behavior is explored, and the results reveal that the arrangement and connection strategy of the GLRs determine the stopband characteristics. Multiple resonators connected in series lead to an increased number of stopbands and more pronounced attenuation valleys, whereas multiple resonators connected in parallel or arranged in a periodic array result in an unchanged number of stopbands but a significantly wider stopband bandwidth. Furthermore, transmission characteristic assessments substantiate the vibration dampening efficacy of GLRs, and the marked suppressions in flexural wave propagation are demonstrated within the multiple merged bandgaps. These insights advance the comprehension of localized resonance phenomena in metamaterials and inform the development of sophisticated noise and vibration control strategies.

中文翻译：

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多带隙中超材料板的振动声学抑制


本文深入探讨了与分组局部谐振器 （GLR） 集成的超材料板的振动和声辐射特性。GLR 由多个弹簧质量谐振器组成，以各种配置（如串联、并联和周期排列）排列，被证明对板的结构性能有显着影响。实现了一个先进的傅里叶级数来阐明板的位移函数和表面声压。利用能量原理，建立了一个振动-声学耦合模型来描述超材料板与外部声场之间的相互作用。该理论框架针对有限元方法仿真进行了严格验证，产生了高度一致的结果。探讨了局部谐振带隙行为，结果表明 GLR 的排列和连接策略决定了阻带特性。多个串联的谐振器会导致阻带数量增加和更明显的衰减谷，而多个谐振器并联或以周期性阵列排列会导致阻带数量不变，但阻带带宽明显更宽。此外，传输特性评估证实了 GLR 的减振效果，并且在多个合并带隙中证明了弯曲波传播的显着抑制。这些见解促进了对超材料中局部共振现象的理解，并为复杂的噪声和振动控制策略的开发提供了信息。