Low-Frequency Optimization and Vibration Reduction Performance of a Nonlinear Small-Sized Cantilever Beam Absorber with Magnets

The low-frequency optimization method and broadband vibration attenuation performance of a small-size nonlinear cantilever beam absorber with magnets are investigated in the paper. By employing the boundary optimization method, the nature frequency of the cantilever beam absorber is reduced by 35.33%, while the reliability of the optimized structure is verified by means of fatigue analysis. Through fitting a nonlinear magnetic force and constructing a vibration reduction system, the vibration suppression performance of a nonlinear magnetic cantilever beam absorber is investigated based on the incremental harmonic equilibrium (IHB) method with an arc-length continuation technique. Then, the influence of the nonlinear absorber parameters on the vibration reduction performance is discussed in detail separately. Finally, relevant experiments are designed to verify the results of the theoretical analysis. The results reveal that the nonlinear stiffness, mass ratio, and damping ratio of the nonlinear absorber significantly affect the vibration reduction characteristics of the main vibration system, and the introduction of the nonlinear parameters changes the vibration reduction frequency and the resonance peak value of the linear absorber, and achieves the expansion of the vibration reduction bandgap in comparison with the linear absorber. These findings can provide a valuable reference for the design of low-frequency and small-size absorbers, as well as the widening of low-frequency damping bandgaps.