Onset of wavenumber bandgaps via alternating Willis coupling signs

TL;DR

This paper presents a method to induce wavenumber bandgaps in elastic media by alternating the signs of Willis coupling in layered structures, revealing new ways to control wave propagation.

Contribution

It introduces a novel unit cell design with alternating Willis coupling signs to analytically predict and create wavenumber bandgaps in elastic materials.

Findings

Wavenumber bandgaps can be achieved with alternating Willis coupling signs.

The bandgap width and limits are analytically derived.

Reversed-sign Willis materials resemble bi-layered phononic crystals.

Abstract

This article introduces a methodology for inducing wavenumber bandgaps via alternating Willis coupling signs. A non-reciprocal wave equation of Willis-type is first considered, and its wave dispersion analyses are carried out via the transfer matrix method. By creating unit cells from two identical Willis-type elastic layers, yet with reversed Willis-coupling signs, a reciprocal band structure peculiarly emerges, although each layer exhibits non-reciprocity if considered individually. Wavenumber bandgaps open due to such unit cell configuration, and their width and limits are analytically quantified. Similarities between materials with reversed-sign Willis coupling and bi-layered phononic crystals are noted, followed by concluding remarks.