Small-world based interactions in elastic metamaterials

The problem of wave propagation control in one-dimensional systems, characterized by long-range interactions, has been the main topic of several publications in recent years. The introduction of magnetostatic or electrostatic forces modify the conventional connectivity based on the short-range interaction, classically studied in structural mechanics. The present paper provides a new definition of long-range force, based on the concept of small-world network. The small-world model, born in the field of social networks, is herein suitably applied to a regular lattice by the introduction of additional, randomly selected, elastic connections between different points, which modify the waves propagation within the structure. It is shown that the modified system exhibits a much higher propagation speed, one of the remarkable characteristic of the newly defined metamaterial or in general multi-DOF s system.