Tunable bandgaps of a metamaterial beam with nonlinear magnetic resonators

This paper presents a metamaterial beam with the nonlinear magnetic mass-beam (NMMB) resonators to achieve certain tunable bandgaps. The metamaterial beam consists of the upper and lower faceplates and the periodically arranged NMMB resonators. The dispersion relation of the infinite-size beam is derived via the energy method. The governing equations of motion of the beam with finite length are obtained based on the Galerkin method. An experiment is designed and the revealed phenomena reach a good agreement with the theoretical analysis and numerical simulations. The results show that the tunable bandgaps are associated with the external excitation amplitude. As the amplitude of the excitation varies, the location and width of the bandgaps can be adjusted according to the frequency shift and multi-bandgap effects. Moreover, the influences of the thickness of the faceplates and the stiffness of cantilevers in the resonators on the bandgaps are shown.