Uncertain acoustic meta-atoms

Acoustic metamaterials (AMMs) consist of periodic arrangements of single meta-atoms (e.g. Brillouin zones). The AMMs can manipulate the acoustic wave propagation in ways that are not found in nature or conventional materials. Furthermore, AMMs can have unnatural material properties such as a negative effective mass or band gaps. One type of meta-atom is based on the principle of a Helmholtz resonator that is embedded in a fluid matrix. A periodic arrangement of such meta-atoms in the two dimensional space combines the effects of a resonator and those of phononic crystals. The effectiveness of that kind of AMM depends on the eigenfrequencies of the resonators and the relative position of one meta-atom to one another. Since the production of AMMs is linked to manufacturing tolerances the perfect periodicity is not fulfilled and can affect the properties of the AMM. This work deals with the uncertainties of the meta-atoms concerning the geometry of the embedded resonator. The uncertain geometry parameters are approximated by spectral expansions combined with the non-intrusive collocation method. Further, the transfer function and the insertion loss with respect to the uncertain parameters are analyzed. Finally, the results of the spectral approach are compared to those of the Monte Carlo method.