Broadband vibration attenuation in nonlinear meta-structures with magnet coupling mechanism: Theory and experiments

Nonlinear metamaterial structures may provide extensive applications in low-frequency and broadband vibration attenuation. Recently, there has been growing interest in nonlinear resonator design towards vibration attenuation of metamaterial structures. This work is focused on investigating the working mechanism of meta-beam by periodically attaching nonlinear coupling multi-frequency resonators for vibration suppression. The Harmonic Balance Method (HBM) and the energy method are first used to obtain theoretical expressions for the edge frequencies of the coupling multi-frequency band gaps. Additionally, the nonlinear coupling 2-DOF (degree of freedom) resonator attached to the primary beam is experimentally designed as a double cantilevered beam with different masses attached to both ends and whose coupling force is achieved by magnet masses on the same plane. The nonlinear coupling behaviors of the frequency response obtained by experimental test agree well with the theoretical analysis of steady-state displacements at different excitation levels. Finally, the dispersion properties of coupling band gaps and the nonlinear dynamic behavior of a finite-sized meta-beam are also investigated. Results show that compared to its rival linear metamaterial structures, the proposed nonlinear meta-beam can obtain a lower-frequency band gap. Furthermore, the nonlinearity of the proposed meta-beam can form broadband vibration attenuation by large excitation level. •A meta-beam mathematical model with nonlinear coupling 2-DOF resonators.•Coupling multiple band-gap formations.•Nonlinear dynamic behaviors of a finite-sized meta-beam with coupling 2-DOF resonators.•Design of the double cantilevered beam resonator with magnet coupling mechanism.•Experimental frequency response is obtained through established vibrational test system to verify the theoretical model.