Localised bending modes in split ring resonators

We present band diagrams for in-plane elastic waves propagating within a doubly periodic structure involving split ring resonators (SRR). From the Navier equations we derive that the lowest resonant frequencies are associated with localised bending modes solutions of a fourth-order differential equation in thin-bridges, which are responsible for the appearance of a low frequency stop band. Potential applications lie in the design of earthquake resistant systems.