Wave attenuation and trapping in 3D printed cantilever-in-mass metamaterials with spatially correlated variability

Abstract

Additive manufacturing has become a fundamental tool to fabricate and experimentally investigate mechanical metamaterials and phononic crystals. However, this manufacturing process produces spatially correlated variability that breaks the translational periodicity, which might compromise the wave propagation performance of metamaterials. We demonstrate that the vibration attenuation profile is strictly related to the spatial profile of the variability, and that there exists an optimal disorder degree below which the attenuation bandwidth widens; for high disorder levels, the band gap mistuning annihilates the overall attenuation. The variability also induces a spatially variant locally resonant band gap that progressively slow down the group velocity until an almost zero value, giving rise to wave trapping effect near the lower band gap boundary. Inspired by this wave trapping phenomenon, a rainbow metamaterial with linear spatial-frequency trapping is also proposed, which have potential applications in energy harvesting, spatial wave filtering and non-destructive evaluation at low frequency. This report provides a deeper understanding of the differences between numerical simulations using nominal designed properties and experimental analysis of metamaterials constructed in 3D printing. These analysis and results may extend to phononic crystals and other periodic systems to investigate their wave and dynamic performance as well as robustness under variability.

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

“…It should also be noted that for increasingly steeper variations of the masses of the resonators, there is band gap annihilation related to the level of disorder degree. It has been shown that this is caused by internal wave trapping phenomena [52] due to the existing critical sections, i.e. local changes from propagating to nonpropagating waves [53].…”

Optimal design of rainbow elastic metamaterials

“…The differences between the experimental and analytical results are mainly the bandgap frequencies, which might be caused by the uncertainties of experimental conditions and 3D manufacturing process. Especially, the dimension and physical parameter variabilities introduced by the 3D printing process are found to have greatly influenced the FRFs of rainbow metamaterial [51], which will be explored specifically in further work.…”

Uncertainties in the attenuation performance of a multi-frequency metastructure from additive manufacturing

“…Currently, there is few experimental work available in the literature investigating metamaterial performance for vibration attenuation applications (e.g. [5][6][7][8][9][10]) and most of them do not consider the effects of spatially correlated disorder on the band gap.…”

“…Multi-resonators design have also been explored in more complex structures with encouraging results for industrial applications [9,10]. It has been shown that the break of periodicity introduced by the spatial variability of material and geometrical properties of metastructures creates a resonator mistuning which can induce wave trapping and thus greatly affecting the vibration attenuation performance by either band gap annihilation or attenuation bandwidth widening, depending on the imposed spatial profile [6]. Overall, there is a need to investigate the effects of the manufacturing variability on the performance of metastructures [1,[26][27][28][29], which can also affect the coupling of the metastructures to the vibration source and receiver [30].…”