Supplemental damping and energy dissipation of structural systems installed with viscous dampers considering connection stiffness

In practice, the supplemental damping performance provided by viscous dampers is affected by the stiffness of connection elements. To explore the influence of the connection stiffness on the supplemental damping and energy dissipation of building structures, the analytical expressions linking the supplemental damping and energy dissipation to the connection stiffness are formulated in this study. These expressions are derived from the harmonic response analysis of the established analysis model which incorporates the classical Maxwell model. Furthermore, the parameter relationships in the suggested analytical expressions are innovatively normalized, thereby allowing for a rapid estimation of the supplemental damping and its efficiency. The normalization also provides concise descriptions of the supplemental damping variation caused by the connection stiffness and damper viscosity. The analysis results support that the damper viscosity should match the connection stiffness; otherwise, excessively improving damper viscosity could cause a counterintuitive decline in the damping effect. The proposed damping evaluation method is then extended to multi-story structures. It is found that the energy dissipation efficiency of installed dampers is not fully guaranteed by the ratio of the connection stiffness to the story lateral stiffness. Finally, the optimization problem of maximizing the energy dissipation index under the efficiency constraint is formulated and completely solved. The proposed optimization approach yields the exact optimal solutions. Note that all the achieved results are rooted in the dynamic properties of linear viscous dampers.