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 cannot be found in nature or conventional materials. Furthermore, AMMs possess unnatural material properties such as a negative effective mass or band gaps. The working principle of the AMMs is frequency dependent and is on the one side based on the principle of a resonator and on the other side based on the principle of interference. Certain parameters for the numerical simulation are considered random and are approximated by spectral expansions, since the production of AMMs is linked to manufacturing tolerances and material inhomogeneities. Hence, a realistic effective working range of the AMMs can be identified.