Uncertainty quantification of acoustic metamaterial bandgaps with stochastic material properties and geometric defects

• Published in: Computers & structures Vol. 305; p. 107511
• Main Authors: Zhang, Han, Mahabadi, Rayehe Karimi, Rudin, Cynthia, Guilleminot, Johann, Brinson, L. Catherine
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2024
• Subjects: Acoustics; Metamaterials; Polynomial chaos expansion; Spectral projection; Uncertainty quantification; Uncertainty quantification; Metamaterials; Acoustics; Spectral projection; Polynomial chaos expansion
• ISSN: 0045-7949
• DOI: 10.1016/j.compstruc.2024.107511

Acoustic metamaterials are a subject of increasing study and utility. Through designed combinations of geometries with material properties, acoustic metamaterials can be built to arbitrarily manipulate acoustic waves for various applications. Despite the theoretical advances in this field, however, acoustic metamaterials have seen limited penetration into industry and commercial use. This is largely due to the difficulty of manufacturing the intricate geometries that are integral to their function and the sensitivity of metamaterial designs to material batch variability and manufacturing defects. Capturing the effects of stochastic material properties and geometric defects requires empirical testing of manufactured samples, but this can quickly become prohibitively expensive with higher precision requirements or with an increasing number of input variables. This paper demonstrates how uncertainty quantification techniques, and more specifically the use of polynomial chaos expansions and spectral projections, can be used to greatly reduce sampling needs for characterizing acoustic metamaterial dispersion curves. With a novel method of encoding geometric defects in a 1D, interpretable, resolution-independent way, our uncertainty quantification approach allows for both stochastic material properties and geometric defects to be considered simultaneously. Two to three orders of magnitude sampling reductions down to ∼100 and ∼101 were achieved in 1D and 7D input space scenarios, respectively. Remarkably, this reduction in sampling was possible while preserving accurate output probability distributions of the metamaterial performance characteristics (bandgap size and location). •Effects of stochastic geometry & materials quantified on metamaterial band gaps.•100× sampling reductions over random sampling in capturing probability distributions.•Single dimensional parameter for generating random manufacturing geometry defects.