Clearance-type nonlinear metastructure for broadband vibration suppression: theory and experiment

To achieve broadband vibration suppression in engineering structures, a novel nonlinear metastructure incorporating clearance-type nonlinear oscillators (CNOs) is proposed, which overcomes the limitation of traditional nonlinear stiffness design. The CNO consists of distributed cantilever beams and stepped mass block, providing segmental stiffness and segmental clearance, respectively. The governing equations of the clearance-type nonlinear metastructure are derived based on the Lagrange equations, and the expression of nonlinear bandgap is obtained by using a semi-analytical method. Notably, there exists a chaotic response band after the bandgap, which significantly attenuates the vibration responses of the host structure. Since the response peaks on both sides of the linear bandgap are highly dependent on the design frequency of the oscillators, and the chaotic band can effectively reduce the post-bandgap vibration responses. The broadband vibration suppression can be achieved through modulating the design frequency of the CNOs. Experimental validation for the nonlinear metastructure with CNOs demonstrates superior broadband vibration attenuation and exhibits strong agreement with the numerical simulations. Furthermore, the combination designs based on the mode shape distribution of the controlled host structure can enable simultaneous multi-mode vibration suppression. The results indicate that the first-order and second-order vibrations of the host structure are reduced by 85.4% and 97.8%, respectively, compared to the uncontrolled case. This study demonstrates that the proposed clearance-type nonlinear metastructure provides a novel and effective approach for low-frequency and broadband vibration suppression, with significant potential for applications in engineering structures.