Frequency band structure of hierarchical viscoelastic metamaterials

A first order asymptotic homogenization technique is herein proposed for the investigation of wave propagation inside periodic microstructured viscoelastic metamaterials with local resonators. Specifically, in order to characterize the frequency band structure of the periodic metamaterials, an eigenvalue problem in terms of frequency-dependent transfer matrix arises. With the aim of designing high-performance waveguides, a parametric optimization scheme is exploited in order to determine optimal mechanical parameters characterizing a band structure with low-frequency band gaps.