Discrete Euler-Bernoulli Beam Lattices with Beyond Nearest Connections

TL;DR

This paper investigates how extending connections beyond nearest neighbors in discrete Euler-Bernoulli beam lattices affects wave dispersion, revealing new zero group velocity modes driven by mass and rotational inertia interactions.

Contribution

It introduces a generalized dispersion relation for infinite mass-beam chains with arbitrary non-local connections, highlighting the impact on wave dynamics and zero group velocity modes.

Findings

Extended connections modify dispersion relations.

Zero group velocity modes depend on mass and rotational inertia.

Non-local interactions enable control over wave propagation.

Abstract

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.