Improving the control performance of optimal tuned inerter damper via nonlinear eddy current damping

The present study proposes a novel eddy-current-based tuned inerter damper (EC-TID) that integrates the tuned inerter damper (TID) with nonlinear eddy current damping. The inclusion of nonlinear eddy current damping is expected to improve the control performance of optimal TID. In particular, the mechanical model and configuration of proposed EC-TID are introduced in detail. A closed-form solution for EC-TID optimal design in both undamped and damped structures is established based on effective damping ratio enhancement (EDRE) effect. This closed-form solution ensures equivalence of nonlinear eddy current damping through employment of statistical linearization techniques (SLT) with both force-based and energy-based equivalent criteria. The EC-TID control effectiveness obtained through Monte Carlo simulation under white noise excitation, which include effective damping ratio and EDRE effect, verifies the accuracy of the closed-form solution established via SLT, and highlights the importance of a large critical velocity of EC-TID in achieving higher accuracy. Moreover, it has been found that the closed-form solution for EC-TID and eddy-current-based tuned viscous mass damper (EC-TVMD) optimal design exhibit significant similarities when their equivalent damping ratios are identical. Several numerical studies have been conducted to investigate the control performance of EC-TID under real seismic excitations. The results demonstrate that both TID and EC-TID exhibit superior EDRE effects in mitigating the seismic response of structures compared to viscous and eddy current dampers with the same damping parameters. Additionally, EC-TID offers improved performance over TID, including slightly higher effectiveness, pre-designed maximum damping force, and reduced deformation. Noted that EC-TID is more effective than EC-TVMD in reducing structural seismic responses when their equivalent damping ratio is set at 0.03. This finding contrasts with a recent study where TID and tuned viscous mass damper (TVMD) exhibited comparable effectiveness under the same conditions.