2016/08/03 by Andrea Bacigalupo, Giorgio Gnecco, Bacigalupo, Andrea +5
Engineering · #Acoustic Wave Phenomena Research #Numerical methods in engineering #Composite Structure Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1608.01077
The elastic wave propagation is investigated in the beam lattice material\ncharacterized by a square periodic cell with anti-tetrachiral microstructure.\nWith reference to the Floquet-Bloch spectrum, focus is made on the band\nstructure enrichments and modifications which can be achieved by equipping the\ncellular microstructure with tunable local resonators. By virtue of its\ncomposite mechanical nature, the so-built inertial meta-material gains enhanced\ncapacities of passive frequency-band filtering. Indeed the number, placement\nand properties of the inertial resonators can be designed to open, shift and\nenlarge the band gaps between one or more pairs of consecutive branches in the\nfrequency spectrum. In order to improve the meta-material performance, a\nnonlinear optimization problem is formulated. The maximum of the largest band\ngap amplitudes in the low-frequency range is selected as suited objective\nfunction. Proper inequality constraints are introduced to restrict the optimal\nsolutions within a compact set of mechanical and geometric parameters,\nincluding only physically realistic properties of both the lattice and\nresonators. The optimization problems related to full and partial band gaps are\nsolved independently, by means of a globally convergent version of the\nnumerical method of moving asymptotes, combined with a quasi-Monte Carlo\nmulti-start technique. The optimal solutions are discussed and compared from\nthe qualitative and quantitative viewpoints, bringing to light the limits and\npotential of the meta-material performance. The clearest trends emerging from\nthe numerical analyses are pointed out and interpreted from the physical\nviewpoint. Finally, some specific recommendations about the microstructural\ndesign of the meta-material are synthesized.\n