Abstract
The possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. To obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. The equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. The constitutive equation of the beam lattice given by the Authors [15] are then applied and a system of six equations of motion is obtained. The propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained.
Highlights
The constitutive equation of the beam lattice given by the Authors [15] are applied and a system of six equations of motion is obtained
I n recent years a considerable interest in acoustic metamaterials was witnessed by several research, most of them focused to the design of artificial materials having periodic microstructure conceived to get complete sound attenuation for a certain frequency range, namely acoustic wave spectral gap
Sonic crystals with spectral gaps [2] have been developed on the realization that composites with locally resonant structural units may exhibit effective negative elastic constants at certain frequency ranges, as shown by Liu et al [3] and by Huang et al [4,5]
Summary
I n recent years a considerable interest in acoustic metamaterials was witnessed by several research (see for reference [1]), most of them focused to the design of artificial materials having periodic microstructure conceived to get complete sound attenuation for a certain frequency range, namely acoustic wave spectral gap. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments.
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