Dispersion degeneracies and standing modes in flexural waves supported by Rayleigh beam structures

Abstract

The paper presents a novel analysis of Floquet-Bloch flexural waves in a periodic lattice-like structure consisting of flexural beam ligaments. A special feature of this structure is in the presence of the rotational inertia, which is commonly neglected in conventional models of the Euler-Bernoulli type. The dispersion properties of the Rayleigh beam structure with rotational inertia include degeneracies linked to Dirac cones on the dispersion diagrams as well as directional anisotropy and special refraction properties. Steering of Dirac cones is described for rectangular flexural structures with a rotational inertia. Numerical examples for a forced network of Rayleigh and Euler-Bernoulli beams illustrate directional localisation, negative refraction, localisation at an interface and neutrality for propagating plane waves across a structured interface for a frequency range corresponding to a Dirac cone.