Lattice structures have long fascinated physicists and engineers not only because of their outstanding functionalities, but also for their ability to control the propagation of elastic waves. While the study of the relation between the connectivity of these systems and their static properties has a long history that goes back to Maxwell, rules that connect the dynamic response to the network topology have not been established. Here, we demonstrate that by tuning the average connectivity of a beam network , locally resonant band gaps can be generated in the structures without embedding additional resonating units. In particular, a critical threshold for is identified, far from which the band gap size is purely dictated by the global lattice topology. By contrast, near this critical value, the detailed local geometry of the lattice also has strong effects. Moreover, in stark contrast to the static case, we find that the nature of the joints is irrelevant to the dynamic response of the lattices. Our results not only shed new light on the rich dynamic properties of periodic lattices, but also outline a new strategy to manipulate mechanical waves in elastic systems.

https://doi.org/10.1103/PhysRevB.91.020103?_gl=1*o0kdrl*_ga*NTE5NTUzNDM2LjE3MzkyMzgwNjA.*_ga_ZS5V2B2DR1*MTc0MDcwODYwMS4yLjEuMTc0MDcwOTI1OS4wLjAuMjMxNTI5NzU5