Discrete Euler–Bernoulli beam lattices with beyond nearest connections

The propagation of elastic waves on discrete periodic Euler–Bernoulli mass-beam lattices is characterised by the competition between coupled translational and rotational degrees-of-freedom at the mass-beam junctions. We influence the dynamics of this system by coupling junctions with beyond-nearest-neighbour spatial connections, affording freedom over the locality of dispersion extrema in reciprocal space, facilitating the emergence of interesting dispersion relations. A generalised dispersion relation for an infinite monatomic mass-beam chain, with any integer order combination of non-local spatial connections, is presented. We demonstrate that competing power channels, between mass and rotational inertia, drive the position and existence of zero group velocity modes within the first Brillouin zone.