Analysis of Amplification Effect and Optimal Control of the Toggle-Style Negative Stiffness Viscous Damper

Abstract

This paper proposes a new toggle-style negative stiffness viscous damper (TNVD), and evaluates the performance of the TNVD with the displacement amplification factor (fd) and the energy dissipation factor (fE). Firstly, the composition and characteristics of the TNVD are introduced. Subsequently, the displacement amplification factor is introduced to evaluate the displacement amplification ability of the TNVD, and it is decomposed into a geometric amplification factor and an effective displacement coefficient. Then, based on the geometric amplification factor and effective displacement coefficient, the correlation between the TNVD’s displacement amplification ability and inter-story deformation is studied, and an improved TNVD is proposed. By the comparison of the finite element calculation results, it is found that the improved TNVD can utilize the assumption of small structural deformation. After that, the impacts of plentiful aspects, such as the length of the lower connecting rod, the horizontal inclination angle of the lower connecting rod, the inter-story deformation limit, the cross-sectional area of the connecting rod, the damping coefficient, and the negative stiffness on the fd and fE of the improved TNVD, are expounded. The research results show that when the length of the TNVD’s lower connecting rod remains unchanged, the fd and fE present a trend of increasing first and then decreasing with the increase in the horizontal inclination angle of the lower connecting rod. When the inter-story deformation is fixed, there exists an optimal lower connecting rod’s length that satisfies a specific relationship to achieve the optimal geometric amplification factor of the TNVD. By adjusting the damping parameters of the TNVD, we can obtain a better effective displacement coefficient greater than 0.95 in the proposed target region. Meanwhile, the fd and fE increase with the decrease in the negative stiffness. An optimization strategy for the improved TNVD has been proposed to ensure that the TNVD has the characteristics of operational safety, ideal displacement amplification capability, and energy dissipation capability. Furthermore, a multi-objective control design method with an additional improved TNVD structure is proposed. The vibration reduction effect of the structure with the improved TNVD and the effectiveness of the optimization strategy are verified through examples.