Broadband locally resonant metamaterials with graded hierarchical architecture

We investigate the effect of hierarchical designs on the bandgap structure of periodic lattice systems with inner resonators. A detailed parameter study reveals various interesting features of structures with two levels of hierarchy as compared with one level systems with identical static mass. In particular: (i) their overall bandwidth is approximately equal, yet bounded above by the bandwidth of the single-resonator system; (ii) the number of bandgaps increases with the level of hierarchy; and (iii) the spectrum of bandgap frequencies is also enlarged. Taking advantage of these features, we propose graded hierarchical structures with ultra-broadband properties. These designs are validated over analogous continuum models via finite element simulations, demonstrating their capability to overcome the bandwidth narrowness that is typical of resonant metamaterials. Published by AIP Publishing.