This paper presents the improved sound insulation performance obtained from a new type of acoustic metamaterial, built by attaching periodic inertial amplification (IA) mechanisms to a host beam. The IA mechanism is a triangular bar-and-hinge device, which connects a small mass to the host beam at two separate locations. The band structure of a unit-cell and the Sound Transmission Loss (STL) of a finite-length beam are calculated by the spectral element method (SEM), which are validated against finite element references. Numerical simulations show that the STL of the IA acoustic metamaterial beam outperforms that of an ordinary beam across a wide band starting from a very low frequency, which suggests the low-frequency soundproof capacity of the IA acoustic metamaterial beam is greatly enhanced. However, the STL curve also experiences a sudden fall after that band, causing an undesired sound insulation valley. To reveal the underlying physics, the band diagram of the beam is studied together with the trace wavenumber of the incident sound wave. It is found that, due to the collectively amplified inertia of periodic small masses, a wide bandgap is introduced in the band diagram at low frequencies, which effectively suppresses flexural vibration of the beam and eventually leads to the observed STL enhancements. However, as a consequence of this bandgap, band diagram inevitably intersects with acoustic trace wavenumber, creating a coincidence phenomenon. Although happens earlier than classical coincidence, this new coincidence produces a similar STL valley. To mitigate this drawback, a hybrid unit-cell containing two IA mechanisms is designed, which attempts to cover the valley caused by one mechanism with the bandgap induced by the other. The effectiveness of this new design is verified and discussed at last.

本文介绍了通过将周期性惯性放大（IA）机制附加到主梁而构建的新型声学超材料，从而提高了隔音性能。IA机构是一个三角形的杆和铰链装置，可在两个单独的位置将较小的质量块连接到主梁。通过频谱元素方法（SEM）计算了单位单元的能带结构和有限长度束的声传输损耗（STL），并针对有限元参考进行了验证。数值模拟表明，从非常低的频率开始，IA声学超材料梁的STL优于普通波束在宽频带上的STL，这表明IA声学超材料梁的低频隔音能力大大提高。然而，在该频带之后，STL曲线也会突然下降，从而导致不希望的隔音谷。为了揭示底层物理原理，研究了束的能带图以及入射声波的迹线波数。发现，由于周期性小质量的集体放大惯性，在低频下在带图中引入了一个宽带隙，这有效地抑制了光束的弯曲振动，并最终导致观察到的STL增强。然而，由于该带隙，带图不可避免地与声迹波数相交，从而产生了重合现象。尽管比经典巧合更早发生，但这种新巧合产生了一个类似的STL谷。为了减轻这一缺点，设计了一种包含两个IA机制的混合单元电池，它试图用一种机制引起的谷底用另一种机制引起的带隙覆盖。最后验证并讨论了该新设计的有效性。