On band gap predictions for multiresonant metamaterials on plates

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.