Tailoring band gap properties of curved hexagonal lattices with nodal cantilevers

Abstract

Metamaterials find applications across diverse domains such as electromagnetics, elasticity, and acoustics by creating band gaps. Lattice-based metamaterials also exhibit band gaps, which have a great potential to influence engineering design in vibration and noise reduction problems. The geometry of the repetitive unit cell in the lattice plays a crucial role in diversifying the location and number of stop bands across the frequency range. One of the key hurdles is devising unit cell architectures that can effectively suppress vibrations across diverse frequency ranges. This work proposes an innovative two-dimensional hexagonal lattice with tailored band gap characteristics through curved beam members and auxiliary cantilever beams at the nodes. We have thoroughly explored the impact of various design parameters on dispersion characteristics, wave directionality through iso-frequency contours of dispersion surfaces, and the transmission loss considering finite lattice. The investigation demonstrates an improvement in band gap characteristics, indicating the generation of more band gaps across the entire frequency range and the widening of the same. This study has the potential to serve as a future benchmark in the development of lattice-based elastic/acoustic metamaterials, particularly for addressing vibration reduction challenges at user-defined frequencies.