Influence of additive manufacturing variability in elastic band gaps of beams with distributed resonators
Danilo Beli1; J. Roberto Arruda1
1 Faculty of Mechanical Engineering, University of Campinas
doi:10.20906/CPS/USM-2016-0019
Resumo
Phononic crystals and acoustic metamaterials are periodic structures that can exhibit the elastic band gap phenomenon. The former consist of periodically varying material properties or geometry, while the latter consist of periodic boundary conditions or periodically distributed resonators. Both lead to stop bands in specific frequency intervals, where elastic waves become evanescent and, therefore, do not propagate. These structures can find applications in passive vibration and noise control. In this work, a polymer beam with periodically distributed resonators is investigated. Geometric and material variations caused by the additive manufacturing process influence the effectiveness of the band gaps, causing some skepticism about the real possibilities of fabricating metamaterials with 3D printing. Variability analysis is usually performed with sampling methods such as Monte Carlo, where a large number of analyses is necessary. Wave propagation methods such as the Spectral Element Method (SEM) are efficient for this kind of analysis. In the wave approach, only a cell needs to be computed to obtain the dispersion curves, which show the band gaps. SEM can also be used to efficiently compute the forced response of the global structure consisting of a number of quasi periodic cells. In this work some samples of a polymer beam were fabricated on a 3D printer and tested for comparison with numerical predictions. Numerical predictions and experimental results show that band gaps are reasonably robust in the presence of variability in the fabrication process. The attenuation within the band gaps decrease when compared to an exact geometry, but attenuation is still significant. Therefore, manufacturing metamaterials for vibration attenuation with 3D printers seems feasible.
Palavras-chave: Timoshenko beam; spectral element method; acoustic metamaterial; Monte Carlo; uncertainty