Dynamic homogenization of random elastodynamic metamaterials using space–time Fourier transform

Abstract

The dynamic homogenization of metamaterials with transfer matrix-based methods poses significant challenges due to an inherent branch ambiguity associated with the real part of the wavenumber. This problem is exacerbated in the presence of disorder (randomness) in cell geometry or material properties. Disorder necessitates larger domains for homogenization, which increase the range of wavenumbers with a branch ambiguity. To resolve this ambiguity, we utilize a Space–Time Fourier Transform (STFT)-based technique and extract primary parameters such as wavenumber and phase velocity, alongside secondary parameters including effective mass density, elastic modulus, and Willis-coupling terms for 1D multilayer media. A variation-based criterion is used to show that dynamic Representative Volume Element (RVE) can only be defined for the primary parameters. A sensitivity analysis is conducted to show that the coefficient of variation of secondary parameters is not only much higher than that of primary parameters, but also does not decrease by increasing the Statistical Volume Element (SVE) size. Our simulations predict the appearance of minor bandgaps induced by disorder. Phenomena such as blue-shift, widening, and merging of bandgaps are observed in random realizations. The STFT technique predicts homogenized parameters in both passbands, bandgaps, and can naturally be extended to higher dimensional metamaterials.