A Bayesian approach for wavenumber identification of metamaterial beams possessing variability

Abstract Recent developments in additive manufacturing have allowed for a number of innovative designs in elastic metamaterials and phononic crystals used in several applications, including vibration attenuation. Complex geometric patterns that were otherwise very expensive or unpractical to produce are currently feasible. However, the 3D printing also introduces variability, which can greatly affect the dynamic performance of the metastructure. This work investigates the effects of manufacturing variability on the wavenumber identification of beams with evenly attached resonators, produced from Selective Laser Sintering. A combination of a correlation-based technique and a Bayes framework is proposed to identify the effective wavenumber and the most probable values of some of the design parameters. Typically of interest, for vibration attenuation using metamaterials, are the mass ratio and the resonator natural frequency. For this purpose an analytical model is derived, assuming an infinite number of resonators tuned to the same frequency. These parameters can be highly affected by the manufacturing variability because they are dependent on complex geometrical features of the metastructure. It is shown that the proposed approach can estimate the most likely values of the parameters with less than 4% difference when compared to a benchmark approach; the latter is not only more complex and time demanding, but also based on indirect measurements. Understanding the effects of this variability on the wave propagation represents an important step towards proposing robust designs with respect to the attenuation performance.