Damped Bloch wave propagation in periodic architected viscoelastic materials: A Fourier-based scheme with quasi-Monte Carlo integration

This paper investigates the behavior of microstructured viscoelastic metamaterials with complex topologies, focusing on their wave propagation characteristics, specifically the behavior of damped Bloch waves. Fourier-based methods are used to solve the governing dynamic equations, taking into account both spatial and temporal damping effects. The study addresses eigenproblems related to Bloch wave dispersion, with a particular emphasis on rational eigenproblems, which are solved using an enhanced derationalization technique previously proposed by the authors. To efficiently approximate the Fourier coefficients, the technique utilizes the quasi-Monte Carlo integration method, which is particularly effective for complex geometries. An illustrative example based on triply periodic minimal surface structures is provided to demonstrate the effectiveness of the proposed approach. The results highlight the potential of these metamaterials for applications in noise reduction, impact resistance, and other advanced engineering fields.