Balancing static and dynamic performances of TMD with negative stiffness

Recently, negative stiffness (NS) has been applied in dynamic vibration absorbers (DVAs) to achieve better control performance on dynamic responses. However, the adoption of NS may amplify the static response. In engineering practice, when the excitation consists of both static and dynamic components, such as wind load, both static and dynamic performances should be considered in the optimal design method. To the best of our knowledge, this important aspect was rarely investigated in the previous literature. In addition, the installation location of NS also significantly affects the performance and design process. However, studies on the location dependence of NS are currently lacking. In order to address these aspects, the optimal design of tuned mass damper with negative stiffness (NS-TMD) is investigated in this paper. The proposed design method considers arbitrary installation locations and the balance of the dynamic and static performances. Subsequently, considering different dynamic-static proportions in practice, the corresponding analytical optimal solutions and empirical formulas are proposed. Finally, the effectiveness of the proposed method is validated by the time history analysis of a slender chimney under wind load. The results show that the control rates of peak along wind and cross-wind responses reach 35.68% and 62.22%, which are 1.36 (along-wind) and 1.50 (cross-wind) times of the conventional TMD. Moreover, the control performance of NS-TMD with mass ratio mu = 0.01 is close to that of TMD with mu = 0.05, which indicates that NS-TMD is promising to provide a practical light-weighted vibration absorption solution for slender structures.