  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
targetted band gap width, location and the confidence level with which it is
guaranteed. The effect of uncertainties are projected from a Bloch-wave
dispersion analysis of three distinct phononic and resonant cellular
configurations and are further confirmed in the frequency response the finite
structures. The analysis concludes with a unique algorithm intended to guide
the design of metamaterials in the presence of system uncertainties.
