An Analytical Investigation on the Vibration Suppression Performance of the Single-sided Vibro-impact Nonlinear Energy Sink

Purpose:Nonlinear Energy Sink (NES) refers to a light-weight device that can suppress vibrations in a broad band manner, but usually suffers a robustness issue that its efficiency is very sensitive to vibration amplitude. A single-sided vibro-impact NES (SSVI-NES), has been recently proved to be more robust than the common NESs, showing a good potential of being a more effective vibration absorber. However, current investigations generally lack theoretical depth, in this paper, an in-depth theoretical study concerning the non-smooth dynamics in SSVI-NES is carried out, in order to provide strongly interpretable rules for the optimal design of SSVI-NESs.Methods:A 2-DOF coupled system comprising a linear oscillator and a SSVI-NES attachment is considered. Based on the Newton impact law, the non-smooth dynamics of the system is first established in a dimensionless manner and then treated using a multiscale expansion method, allowing one to obtain the slow invariant manifold (SIM) on which the system states could occur. Thanks to the SIM, the priodic orbits as well as asymptotic behaviors, are comprehensively studied, to reveal the vibration damping mechanisms of the SSVI-NES.Results:Theoretical and numerical results indicate that the general SSVI-NES (in presence of impact clearance) can achieve optimal vibration suppression efficiency within a relatively large amplitude range. Moreover, due to the stability of SIM, it can converge to the special SSVI-NES (without impact clearance) at the large amplitude level, making the SSVI-NES performs almost linearly to maintain a good robustness with respect to vibration amplitude.