Tunable nonlinear metastructure with periodic bi-linear oscillators for broadband vibration suppression

A novel tunable nonlinear metastructure with periodically distributed bi-linear oscillators (BLOs) is proposed for broadband vibration suppression. The BLO with non-smooth nonlinearity is composed of a cantilever-beam resonator and two limiters, whose tunability for bi-linear stiffness can be achieved by adjusting the clearance size and limiting position. By simplifying the present nonlinear metastructure, we firstly establish a two degrees-of-freedom (2-DOF) dynamic model and analyze its nonlinear dynamic behaviors to reveal the underlying energy transfer mechanism. The governing equations of the nonlinear metastructure integrated with BLOs are derived using the Hamilton principle. The semi-analytical solutions of the nonlinear bandgap boundaries that depend on the amplitude-clearance ratio and the nonlinear stiffness ratio are derived to evaluate the bandgap behavior of the nonlinear metastructure, which is validated well by comparing with the frequency-response behavior of the metastructure using its analytical model and finite element model. The numerical simulation results show that the tunable-nonlinear-bandgap characteristic of the proposed metastructure can be achieved by modulating the clearance size and the nonlinear stiffness of the BLOs. In particular, a nonlinear bandgap possessing substantial amplitude reduction can be observed, which makes the nonlinear metastructure behave excellent broadband vibration suppression performance. Furthermore, there exist a minimum number of BLOs with a small additional mass which can form a dramatic vibration reduction for practical design with finite-size metastructure. The present work demonstrates that the designed tunable-BLOs-based metastructure with non-smooth nonlinearity can contribute to a breakthrough of the limitation of existing nonlinear metastructure and provide a novel and effective approach to tailor strong mechanical nonlinearity and to enhance broadband vibration attenuation performance.