Widely tunable magnetorheological metamaterials with nonlinear amplification mechanism

This paper proposes the design of an active nonlinear metamaterial for broadband and tunable low-frequency wave attenuation governed by a lever-based nonlinear amplification mechanism and a varying stiffness of a magnetorheological elastomer (MRE) driven by an external magnetic field. The metamaterial is formed by periodical spring-lever-MRE resonators connected to a base beam. Its strongly nonlinear behavior is described by a nonlinear amplification factor that depends on a magnetic flux density, a lever ratio, and an excitation amplitude. We use the Galerkin method to theoretically study the tunability of a low-frequency bandgap in terms of the MRE properties and the nonlinear amplification conditions. The obtained results are validated in numerical simulations. We also explore the mechanisms for broadband low-frequency wave attenuation governed by the strongly nonlinear dynamics of the proposed metabeam. Our results show that the metabeam with a large lever ratio can achieve substantial shifts of the bandgap frequencies for reasonably small variations of excitation amplitudes, while the bandgap size can be actively changed by varying the magnetic flux density. Our metamaterial is thus a promising solution to realize adaptive and actively tunable wave-attenuating metastructures that could be beneficial for practical applications.