Bistable enhanced passive absorber based on integration of nonlinear energy sink with acoustic black hole beam

Abstract

The nonlinear energy sink (NES) has a broader frequency bandwidth than the linear tuned-mass-damper (TMD), making it more robust. However, the NES is only efficient in a narrow energy range. The mitigation property of NES may deteriorate when input energy is too small or large. To overcome this shortage, a novel NES named ABH-BNES is proposed in this paper, by combining a bistable nonlinear energy sink (BNES, which has negative linear stiffness, cubic nonlinear stiffness, and linear damping) and acoustic black hole (ABH) beam. The negative linear stiffness and cubic nonlinear stiffness elements can generate a large cross-well motion to improve the performance of vibration mitigation for low input energy. By replacing the attached mass in traditional NES as an ABH beam, multiple high-damping modes can be introduced into the vibration absorber. So that the performance of ABH-BNES is also enhanced for large input energy. First, the Gaussian Expansion Method and Modal Approach are employed to establish the dynamic model of a single-dof linear oscillator coupling with an ABH-BNES. Such a modeling approach is verified by comparing it with the models in the existing literature and established by the finite element method (FEM). The slow invariant flow (SIM) theory and time-domain integration are employed to analyze the novel NES's vibration mitigation mechanism. In addition, a multi-solution boundary related to the existence of targeted energy transfer is derived for optimizing the nonlinear absorber. Then, the energy method is used to verify the superiority of the novel NES by comparing it with TMD, NES, and the Linear ABH absorber. The results show that the ABH-BNES can behave with an excellent mitigation effect and an extensive energy bandwidth when the parameters are appropriately selected. Finally, an experiment is carried out to verify the new NES's superiority and the correctness of the theoretical model.