Bandgaps in two-dimensional high-contrast periodic elastic beam lattice materials

TL;DR

This paper investigates elastic wave propagation in 2D high-contrast periodic beam lattices, demonstrating how modified homogenization theory can predict bandgaps linked to low-frequency resonances of soft components.

Contribution

It introduces a high-contrast homogenization approach for elastic waves in 2D beam lattices, explicitly relating bandgaps to resonant frequencies of soft components.

Findings

High-contrast homogenization predicts bandgaps in elastic wave spectra.

Explicit example with a resonant beam illustrates the theory.

Bandgaps are linked to low-frequency resonances of soft components.

Abstract

We consider elastic waves in a two-dimensional periodic lattice network of Timoshenko-type beams. We show that for general configurations involving certain highly-contrasting components a high-contrast modification of the homogenization theory is capable of accounting for bandgaps, explicitly relating those to low resonant frequencies of the `soft' components. An explicit example of a square-periodic network of beams with a single isolated resonant beam within a periodicity cell is considered in detail.