A lever-enhanced tuned inerter damper for controlling vibrations due to rotary unbalance and bounded parametric uncertainty: Classic and robust equal-peak optimization

Abstract

This study proposes a lever-enhanced tuned inerter damper (LTID) for controlling the excessive vibrations induced by rotary unbalance within the primary system, whose stiffness is further considered a bounded uncertain parameter. Classic and robust equal-peak optimal design of the proposed LTID are carried out according to the methodologies stemming from the fixed-points phenomenon. Closed-form solutions to the $H_{\infty }$ optimization problem are analytically derived, whose accuracy is validated by comparing with either the long-established results in the literature or exact solutions numerically obtained in this study. Numerical results clearly suggest that in contrast to the classic one, robust equal-peak optimization can always produce the same and minimized vibration amplitude at the leftmost and rightmost peaks, regardless of the stiffness uncertainty magnitude. Compared to the classic LTID, the improvement made by the robust LTID in terms of minimizing and equalizing worst-case vibration amplitudes becomes more evident as the stiffness uncertainty magnitude increases. Meanwhile, the effectiveness of LTID is controlled by the amount of inertance and the lever amplification ratio simultaneously. Finally, the proposed LTID is exempt from the need for a large oscillating mass and is appropriate for lightweight applications of vibration control, as also inferred from the fact that the inerter device could generate an inertance far greater than its physical mass and the amplification ratio of a lever could be easily adjusted by changing the location of its fulcrum.