title: Zero-frequency and slow elastic modes in phononic monolayer granular membranes.
abstract: We theoretically study the dispersion properties of elastic waves in hexagonal and honeycomb monolayer granular membranes with either out-of-plane or in-plane particle motion. The particles interact predominantly via normal and transverse contact rigidities. When rotational degrees of freedom are taken into account, the bending and torsional rigidities of the intergrain contacts can control some of the phononic modes. The existence of zero-frequency modes, zero-group-velocity modes and their transformation into slow propagating phononic modes due to weak bending and torsional intergrain interactions are investigated. We also study the formation and manipulation of Dirac cones and multiple degenerated modes. This could motivate variety of potential applications in elastic waves control by manipulating the contact rigidities in granular phononic crystals.
authors.affiliation: LAUM, UMR-CNRS 6613, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France. Electronic address: liyang.zheng.etu@univ-lemans.fr.
authors.forename: Li-Yang
authors.initials: LY
authors.lastname: Zheng
authors.affiliation: LAUM, UMR-CNRS 6613, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: Hélène
authors.initials: H
authors.lastname: Pichard
authors.affiliation: LAUM, UMR-CNRS 6613, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: Vincent
authors.initials: V
authors.lastname: Tournat
authors.affiliation: LAUM, UMR-CNRS 6613, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France.
authors.forename: Georgios
authors.initials: G
authors.lastname: Theocharis
authors.affiliation: LAUM, UMR-CNRS 6613, Université du Maine, Av. O. Messiaen, 72085 Le Mans, France. Electronic address: vitali.goussev@univ-lemans.fr.
authors.forename: Vitalyi
authors.initials: V
authors.lastname: Gusev
keywords: Granular phononic crystal; Zero-frequency modes