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

TL;DR

This paper investigates the unique dispersion characteristics of Rayleigh beam structures with rotational inertia, revealing degeneracies, Dirac cones, and anisotropic wave behaviors that influence wave propagation and localization.

Contribution

It introduces a novel analysis of Floquet-Bloch flexural waves in Rayleigh beam lattices, highlighting the effects of rotational inertia on dispersion and wave phenomena.

Findings

Presence of Dirac cone degeneracies in dispersion diagrams

Directional anisotropy and special refraction properties observed

Numerical examples show wave localization, negative refraction, and interface effects

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.