Elastic wave attenuation in a metaplate with periodic hollow shapes for vibration suppression

Low noise and vibrations are requirements for engineering structures to realize comfort and ensure systems are environmental friendly. Periodic structures such as phononic crystals have been investigated to suppress noise and vibrations because they inhibit elastic wave propagation in the frequency ranges referred to as the band gap. This study led to the proposal of a metaplate (MP) with periodic hollow structures to form band gaps by changing the surface shapes of the thin plates. MPs such as this can be beneficial from the viewpoints of manufacturing cost and structural reliability when applied to engineering structures. To evaluate the potential ability of the proposed MP to suppress vibrations, we obtained the band gap frequency of out-of-plane deformation waves using the wave finite element method. To efficiently evaluate the band gaps, the internal degrees of freedom in a unit cell are reduced based on the modal analysis technique. Furthermore, the out-of-plane and in-plane deformation waves are separated using kinematic energy to extract the band gap related to the out-of-plane deformation waves. Based on this numerical framework, we demonstrate that periodic hollow shapes can form a band gap in the frequency range of interest in engineering problems. Moreover, the potential of the MP was investigated using hollow shape design and material selection, and the results indicate that the proposed MP is beneficial for tuning the band gap frequency in a unit cell of which the size is acceptable for engineering structures. Finally, vibration suppression caused by band gap is experimentally demonstrated via impact testing of an MP fabricated using additive manufacturing.

Automated summary

Low noise and vibrations are important for comfortable and environmentally friendly engineering structures. Periodic structures like phononic crystals can effectively suppress noise and vibrations by creating band gaps. This study proposes a metaplate (MP) with periodic hollow structures, which can form band gaps by changing the surface shapes of thin plates. Numerical simulations and experimental results demonstrate that the proposed MP has the potential to tune band gap frequencies and suppress vibrations in engineering structures.