Uncertainty quantification of tunable elastic metamaterials using polynomial chaos

Owing to their periodic and intricate configurations, metamaterials engineered for acoustic and elastic wave control inevitably suffer from manufacturing anomalies and deviate from theoretical dispersion predictions. This work exploits the Polynomial Chaos Theory to quantify the magnitude and extent of these deviations and assess their impact on the desired behavior. It is shown that uncertainties stemming from surface roughness, tolerances, and other inconsistencies in a metamaterial's unit-cell parameters alter the targeted bandgap width, frequency range, and the confidence level with which it is guaranteed. The effect of uncertainties is projected from a Bloch-wave dispersion analysis of three distinct phononic and resonant cellular configurations and is further confirmed in the frequency response of the finite structures. The analysis concludes with a unique algorithm intended to guide the design of metamaterials in the presence of system uncertainties.