Optimal design of tuned viscous mass damper for acceleration response control of civil structures under seismic excitations

The tuned viscous mass damper (TVMD) is one of the effective inerter-based systems for vibration control of civil structures. TVMD is composed of an inerter, a spring, and an energy dissipation element (EDE). Although the optimal design of TVMD has already been well investigated, the research findings focusing on the TVMD design for acceleration response control of the primary structure under seismic excitations are sparse. In this study, three closed-form solutions of TVMD optimal design parameters are proposed under the hypothesis of harmonic and white noise seismic excitation to mitigate the acceleration response of the undamped primary structure. Numerical analysis results indicate that the proposed closed-form solutions can still provide a good estimating of the TVMD optimal design parameters for the lightly damped primary structure whose damping ratio is less than 0.05. The control performance of TVMD is regarded as the effective damping ratio added to the primary structure, and the analytical expression of the effective damping ratio of TVMD is therefore derived. Further, a novel concept of effective damping ratio enhancement (EDRE) effect is proposed to explain the better control performance of a TVMD than a bare EDE with the same damping coefficient. It is found that TVMD designed by the proposed closed-form solutions (with the hypothesis of white noise seismic excitation) can ensure its better control performance than a bare EDE with the same damping coefficient. The control performance of three TVMDs (named as TVMD1, TVMD2, and TVMD3, respectively) designed by the proposed closed-form solutions is eventually corroborated by twenty sets of real seismic ground motions. The results show that TVMD2 is the most economical and efficient control scheme for structural seismic response control. Combining with the restricted condition for the proposed closed-form solutions, TVMD1 is still recommended in the case of mass ratio in the range of 0.25 to 0.50. If the higher control performance of TVMD is expected with its damping ratio larger than 0.125, TVMD3 is a better choice.