Modeling and performance of a metamaterial beam with magnetically coupled resonators

During the past decade, structural nonlinearities have been utilized to widen the bandgaps of locally resonant metamaterials. In this paper, a novel metamaterial beam with nonlinear coupled oscillators as its local resonator is developed to enlarge the low-frequency bandgaps. First, the governing equations of the magnetically coupled metamaterial beam are established based on the Euler-Bernoulli theory. Subsequently, the transmittance and bandgap properties of such a nonlinear metamaterial beam are studied. It is revealed that by increasing the coupled nonlinear stiffness effectively broadens the low-frequency bandgap. A parametric study is conducted to ascertain the effects of critical parameters, such as coupled nonlinear stiffness, base excitation, and the difference between the two coupled local oscillators, on the bandgaps and vibration suppression performance. It is observed that the coupled nonlinear stiffness has a significant impact on the transmittance of metamaterial beams, while the resonant frequency difference has a relatively minor influence on the transmittance. Meanwhile, the bandgap will shift to high-frequency range as the base excitation increases. Several useful conclusions are summarized and provided as guidelines for further structural optimization and performance enhancement.