Wave dispersion in viscoelastic resonant metamaterials with periodized disordered microstructures

We investigate wave propagation in disordered resonant metamaterials through a stochastic framework based on the toroidal periodization of finite microstructural windows. The approach combines ensemble-averaged asymptotic homogenization in the low-frequency regime with spectral analysis and transmission simulations beyond the homogenization limit. A representative volume element is identified through a convergence analysis of the effective constitutive response over multiple realizations and increasing window sizes. The spectral analysis reveals a pseudodispersion response exhibiting a persistent attenuation interval that remains essentially invariant with respect to the size of the periodized window. Spectral decomposition and longitudinaltransverse hybridization analyses show that this attenuation regime originates from a loss of coherent plane-wave content caused by the interaction between propagating waves and localized resonant modes, and is therefore interpreted as a hybridization-induced pseudo-gap. Independent transmission simulations show a marked reduction of coherent wave transmission at an excitation frequency within the spectrally identified attenuation region, providing a complementary dynamic check of the local-resonance mechanism. The proposed framework provides a consistent route for linking stochastic homogenization, spectral characterization, and wave attenuation in non-periodic resonant metamaterials.