Optimal semi-active vibration absorber for harmonic excitation based on controlled semi-active damper

The semi-active vibration absorber (SVA) based on controlled semi-active damper is formulated to realize the behaviour of the passive undamped vibration absorber tuned to the actual harmonic disturbing frequency. It is shown that the controlled stiffness force, which is emulated by the semi-active damper to realize the precise real-time frequency tuning of the SVA, is unpreventably combined with the generation of undesirable damping in the semi-active damper whereby the SVA does not behave as targeted. The semi-active stiffness force is therefore optimized for minimum primary structure response. The results point out that the optimal semi-active stiffness force reduces the undesirable energy dissipation in the SVA at the expenses of slight imprecise frequency tuning. Based on these findings, a real-time applicable suboptimal SVA is formulated that also takes the relative motion constraint of real mass dampers into account. The results demonstrate that the performance of the suboptimal SVA is closer to that of the active solution than that of the passive mass damper.