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The elastic wave propagation is investigated in the beam lattice materialcharacterized by a square periodic cell with anti-tetrachiral microstructure.With reference to the Floquet-Bloch spectrum, focus is made on the bandstructure enrichments and modifications which can be achieved by equipping thecellular microstructure with tunable local resonators. By virtue of itscomposite mechanical nature, the so-built inertial meta-material gains enhancedcapacities of passive frequency-band filtering. Indeed the number, placementand properties of the inertial resonators can be designed to open, shift andenlarge the band gaps between one or more pairs of consecutive branches in thefrequency spectrum. In order to improve the meta-material performance, anonlinear optimization problem is formulated. The maximum of the largest bandgap amplitudes in the low-frequency range is selected as suited objectivefunction. Proper inequality constraints are introduced to restrict the optimalsolutions within a compact set of mechanical and geometric parameters,including only physically realistic properties of both the lattice andresonators. The optimization problems related to full and partial band gaps aresolved independently, by means of a globally convergent version of thenumerical method of moving asymptotes, combined with a quasi-Monte Carlomulti-start technique. The optimal solutions are discussed and compared fromthe qualitative and quantitative viewpoints, bringing to light the limits andpotential of the meta-material performance. The clearest trends emerging fromthe numerical analyses are pointed out and interpreted from the physicalviewpoint. Finally, some specific recommendations about the microstructuraldesign of the meta-material are synthesized.

Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials