Research on Dynamics Characteristics of Grounded Damping Nonlinear Energy Sink

The nonlinear energy sink (NES) system mainly dissipates energy through damping elements, and changing the position of the damping element will also change the performance of the NES. In this paper, a grounded damping NES is proposed by grounding the damping element of the traditional cubic stiffness NES. The complex dynamics of this two-degree-of-freedom system are investigated. The slow-varying equations of the system under 1:1 internal resonance are derived by using the complexification-averaging (C×A) method, based on which the influence of the primary structure’s damping on a bifurcation is analyzed. The conditions for the existence of strongly modulated response (SMR) are studied, and the accuracy of the results is verified using the slow invariant manifold (SIM), Poincare mapping, and time-history diagrams. This provides a means of verifying the analytical findings. The vibration suppression effects of the grounded damping NES, as compared to the cubic stiffness NES, are thoroughly studied under both pulse and harmonic excitations. The results indicate that the main structure damping affects the stability of the system and the occurrence of the SMR. Most previous studies of the NESs have overlooked the effect of main structure damping, which may influence the selection of structural parameters. Moreover, under relatively large pulse or harmonic excitations, the vibration suppression effectiveness of the grounded damping NES surpasses that of traditional cubic stiffness NES. This finding has important practical significance for improving the vibration suppression effect and robustness of the NES, and provides a reference for the structural design of the NES.