title: On band gap predictions for multiresonant metamaterials on plates.
abstract: Recently wide frequency band gaps were observed in an experimental realization of a multiresonant metamaterial for Lamb waves propagating in thin plates. The band gaps rose from hybridization between the flexural plate (A0 Lamb waves) and longitudinal resonances in rods attached perpendicularly. Shortly thereafter a theory based on considering a one-dimensional periodic array of rods and the scattering matrix for a single rod successfully described the observations. This letter presents an alternative simpler theory, arguably accurate at high rod density, that treats the full two-dimensional array of rods and makes no assumption of periodicity. This theory also fits the measurements.
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: John Y
authors.initials: JY
authors.lastname: Yoritomo
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: Richard L
authors.initials: RL
authors.lastname: Weaver
authors.affiliation: ISTerre, Universite Joseph Fourier, Grenoble, Boîte Postale 53 38041, Grenoble Cedex 9, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Roux
authors.affiliation: Institut Langevin, Ecole Supérieure de Physique et de Chimie Industrielles de la ville de Paris and Centre National de la Recherche Scientifique, Unités Mixtes de Recherche 7587, L'université de Recherche Paris Sciences et Lettres, 1 Rue Jussieu, 75005, Paris, France.
authors.forename: Matthieu
authors.initials: M
authors.lastname: Rupin
authors.affiliation: Acoustics Division, Code 7106, Naval Research Laboratory, 4555 Overlook Avenue, Washington, DC 20375, USA.
authors.forename: Earl G
authors.initials: EG
authors.lastname: Williams