Broadband multifrequency vibration attenuation of an acoustic metamaterial beam with two-degree-of-freedom nonlinear bistable absorbers

In this study, we propose an acoustic metamaterial beam with periodically mounted two-degree-of-freedom (2-DOF) nonlinear bistable absorbers (TNBA) to achieve broadband multi-frequency vibration attenuation. Linearization of the TNBA is made based on bistable nonlinearity, i.e., small-amplitude intra-well responses and large-amplitude inter-well responses. The linear and nonlinear dynamic characteristics of TNBA correspond to linearized (LAMB) and nonlinear (NAMB) acoustic metamaterial beam, respectively. For LAMB, both the averaging-material-properties-based model and the transfer matrix method are employed to study the intra-well responses of the TNBA and explore the mechanism of the two locally resonant (LR) stopbands. Combining the negative effective mass model, augmenting either mass or stiffness is an effective approach to widen the bandwidth of stopbands and enhance the vibration attenuation performance. For NAMB, the finite element method is utilized to calculate the transmission coefficient of a series of finite-length NAMBs with a finite number of TNBAs. The dynamic characteristics of TNBA are investigated. Two LR stopbands in the nonlinear structure are wider than those in the linear counterpart. This is because the TNBA could exhibit both intra-well and inter-well responses under vertical excitations, which can absorb greater kinetic energy from the host beam and lead to more prominent vibration attenuation of the host beam. Metamaterials based on multi-DOF nonlinear absorbers have great prospects in the field of vibration and noise attenuation fields.