Abstract
A parametric beam lattice model is formulated to analyze the propagation properties of elastic in-plane waves in an auxetic material based on a hexachiral topology of the periodic cell, equipped with inertial local resonators. The Floquet–Bloch boundary conditions are imposed on a low-order linear model, suitably reduced to the only dynamically active degrees-of-freedom through a quasistatic stiffness condensation. Since the resonators can be designed to open and shift band gaps, an optimal design, focused on the largest possible gap in the low-frequency range, is achieved by solving a maximization problem in the bounded space of the significant geometrical and mechanical parameters. A local optimized solution, for the lowest pair of consecutive dispersion curves, is found by employing the globally convergent version of the method of moving asymptotes, combined with Monte Carlo and quasi-Monte Carlo multi-start techniques.
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