Optimal design of tuned viscous mass dampers based on effective damping ratio enhancement effect

This paper proposes a novel concept of the effective damping ratio enhancement (EDRE) effect to describe the better seismic control performance of a tuned viscous mass damper (TVMD) compared to a bare energy dissipation element (EDE) with the same damping coefficient, in which the TVMD control performance is regarded as an effective damping ratio added to the primary structure. The analytical expression of the TVMD effective damping ratio is derived for the primary structure subjected to the white noise excitations. The essential relationship between the response mitigation ratio, effective damping ratio, and the EDRE factor is revealed via theoretical derivation and parametric study. Moreover, a closed-form solution of TVMD optimal design parameters is proposed to obtain the maximum value of the EDRE factor and effective damping ratio. In contrast with the classical fixed-point solution, the TVMD designed by the proposed closed-form solution has an improved control performance level. Additionally, the optimal EDRE effect is obtained with a lower damping coefficient when the mass ratio is below 0.20. The proposed closed-form solution can ensure the control performance of TVMD better than a bare EDE, making its application more meaningful. The TVMD design procedure based on the EDRE effect is eventually established. Several numerical examples are conducted to verify the proposed TVMD design methodology under the selected real earthquake records. Time-domain analysis results show that the TVMD control performance is improved by the composite effect of its energy dissipation performance and the reduction in the system input energy, which should be represented by the effective damping ratio and EDRE effect.