Optimal design of the band structure for beam lattice metamaterials

Sonic or acoustic metamaterials may offer a mechanically robust and highly customizable solution to open large band gaps in the low-frequency dispersion spectrum of beam lattice materials. Achieving the largest possible stop bandwidth at the lowest possible center frequency may be a challenging multi-objective optimization issue. The paper presents a first effort of analysis, systematization and synthesis of some recent multi-disciplinary studies focused on the optimal spectral design of beam lattice materials and metamaterials. The design parameter vector is a finite set including all the microstructural properties characterizing the periodic material and the local resonators. Numerical algorithms are employed as leading methodology for solving various instances of the optimization problem. Methodological alternatives, based on perturbation methods and computational modeling, are also illustrated. Some optimal results concerning the dispersion spectrum of hexachiral, tetrachiral and anti-tetrachiral materials and metamaterials are summarized. The concluding remarks are accompanied by preliminary ideas to overcome some operational issues in solving the optimization problem.