Dynamic analysis of single-sided vibro-impact nonlinear energy sinks via forced response curves and application to vibration mitigation

The frequency response mechanisms of the single-sided vibro-impact nonlinear energy sink (SSVI-NES) are comprehensively investigated focusing on the application of passive vibration control. Nonlinear energy sink (NES) refers to a broadband vibration damping technique that was developed based on the targeted energy transfer (TET) of nonlinear systems. The SSVI-NES, which achieves the TET by means of asymmetric single-sided vibro-impacts, can offer improved TET with a faster time scale and enhanced robustness with respect to forcing conditions when compared to other types of NESs that are constructed with smooth nonlinearities. However, the resonance mechanisms and frequency response characteristics of such SSVI-NES, despite special significance in vibration damping analysis, remain an open question due to the difficulties associated with non-smooth terms. In this paper, for the first time, by proposing an alternative frequency–time harmonic balance technique into the Hunt and Crossley vibro-impact model, the forced response curves (FRCs) of such SSVI-NES is calculated, allowing one to uncover the dynamical mechanism of the SSVI-NES and its vibration-damping performance with physical in-depth. Thanks to the FRCs, the resonance mechanisms as well as the bifurcation conditions of the SSVI-NES are then comprehensively investigated with a specific focus paid to the parametric evaluation effects of the forcing amplitude, the stiffness, and the impact loss, revealing the rich response regimes of the SSVI-NES.As a result, a set of easy-to-use design criteria for SSVI-NES is finally obtained to realize vibration suppression over a wider range of forcing amplitudes and frequencies for subsequent generalization to complex structures.