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Tuned viscous mass damper （TVMD） is widely recognized as one of the promising inerter-based devices. This study focused on investigation of the effective damping ratio enhancement effect and optimal design of TVMD for building structures under seismic excitations. The TVMD control performance for the structural inherent damping energy dissipation power was regarded as an effective damping ratio added to the primary structure. Further，a theoretical expression of the TVMD effective damping ratio was derived based on the random vibration theory. To make the application of TVMD more valuable，TVMD was expected to obtain a larger effective damping ratio compared to the viscous damper （VD） with the same damping coefficient，which was defined as the effective damping ratio enhancement effect. The effective damping ratio enhancement factor was introduced for the quantitative evaluation of the enhancement effect on the damping ratio. Both the effective damping ratio and the effective damping ratio enhancement factor were considered as optimization objectives，and a closed-form solution of TVMD optimum design parameters was therefore proposed. Analysis results showed that the proposed closed-form solution had an excellent applicability and stability. The TVMD mass ratio and damping ratio were recommended to be less than 0.3 and 0.1，respectively，for the sake of the best efficiency of the damping ratio enhancement effect. A 7-story steel benchmark model was taken as an engineering example to illustrate the TVMD optimal design process and to verify the validity and superiority of the proposed closed-form solution. It was found that the deformation of the damping element for TVMD designed by the proposed closed-form solution was amplified remarkably，demonstrating the desired effective damping ratio enhancement effect. Most importantly，compared to the traditional closed-form solution，the best advantage of the proposed closed-form solution is to ensure that TVMD control performance is better than VD with the same damping coefficient，regardless of control efficiency problem.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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