Long-range coupling of waveguides

Recently the authors proposed a model and related analysis on waves in long-range metamaterials. Nonlocal elasticity can be produced by several interacting forces acting between particles at long distance, as Coulomb or magnetic-static forces. The chance of introducing this long-distance forces has a disruptive effect in the elastic dynamics. In fact, classical elasticity is based only upon closest particles interaction in which short range-elastic forces act. A particular characteristic of these forces is that they can couple distant structures, as for example two elastic beams or rods, each made of an elastic support with embedded magnets. The interaction produces intra-forces and inter-forces that change the dynamics of the coupled structure. This paper investigates new phenomena that can be observed in such unusual systems, providing a theoretical framework, as well as numerical simulations.