Uncertainty Quantification of Bandgaps in Acoustic Metamaterials with Stochastic Geometric Defects and Material Properties

This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given stochastic material properties and geometric defects. A novel method of encoding geometric defects in an interpretable, resolution independent is showcased in the formation of input space probability distributions. Orders of magnitude sampling reductions down to $\sim {10}^0$ and $\sim {10}^1$ are achieved in the 1D and 7D input space scenarios respectively while maintaining accurate output space probability distributions through combining Monte Carlo, quadrature rule, and sparse grid sampling with surrogate model fitting.