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.