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

Additive manufacturing has been used to propose several designs of phononic crystals and metamaterials 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 metastructures, a well-defined spatial profile. In this work, the effects of the break of periodicity caused by additive manufacturing variability on the attenuation performance of a multi-frequency metastructure is investigated. First, an experimental investigation on the manufacturing tolerances of test samples produced from a Selective Laser Sintering process are assessed and variability levels are used to propose a random field model for the metastructure. Subsequently, the stochastic model is used to investigate the vibration suppression performance of broadband multi-frequency metastructures. An analytical model based on a transfer matrix approach is used to calculate transfer receptance due to a point time harmonic force in a finite length metastructure, which is composed of evenly spaced non-symmetric resonators attached to a beam with H-shaped cross-section. This design creates a multi-frequency metastructure, i.e. band gaps in more than one frequency band. Individual samples of the random fields are used to show that the mistuned resonators can change the vibration attenuation performance of the metastructure and that even small levels of variability, given by less than 1% for the mass and less than 3% for the Young's modulus can have a significant effect on the overall vibration attenuation performance of the metastructure when considered together. It is also shown that different spatial profiles can have a significant effect on the vibration attenuation performance in both band gaps. Therefore, the modelling of the uncertainty metastructures has to take into account the spatial correlation of the properties of the metastructure resonators. The obtained results are expected to be useful for further robust design in mass produced industrial applications. (C) 2019 Elsevier Ltd. All rights reserved.