Response variability of broadband multi- frequency metastructure from additive manufacturing

Additive manufacturing has been used to propose several designs of phononic crystals and metamate-rials due to the low cost to produce complex geometrical features. However, like any other manufacturing process, it can introduce material and geometrical variability in the nominal design and therefore affect the structural dynamic performance. Locally resonant metamaterials are typically designed such that the distributed resonators have the same natural frequency or, in the case of rainbow meta-structures, a well-defined spatial profile. In this work, manufacturing tolerances of beam samples produced from a Selective Laser Sintering process are assessed and variability levels are used to investigate the vibration suppression performance of broadband multi-frequency metastructures. Evenly spaced non-symmetric resonators are attached to a beam with U-shaped cross-section. An analytical model based on a transfer matrix approach is used to calculate transfer receptance due to a point time harmonic force. Moreover, a random field model is assumed based in previous experimental results and the effects of the correlation length, a measure of the spatial fluctuation, are also investigated for individual beams and also in terms of ensemble statistics. The obtained results are expected to be useful for further robust design in mass produced industrial applications.